Quiz:Subgroup structure of special linear group:SL(2,3)

See subgroup structure of special linear group:SL(2,3) for more information.

Basic stuff
$$SL(2,3)$$ has order 24. Summary table on the structure of subgroups:

{What is the relationship between special linear group:SL(2,3) and alternating group:A4? - The latter occurs both as a subgroup and as a quotient group of the former. - The latter is isomorphic to a subgroup of index two in the former, but does not occur as a quotient of the former. + The latter is isomorphic to a quotient of the former by a subgroup of order two, but does not occur as a subgroup. - The latter occurs neither as a subgroup nor as a quotient group of the former.
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{For which of the following divisors of 24 does there not exist a subgroup of $$SL(2,3)$$ of that order? - 2 - 3 - 4 - 6 - 8 + 12
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{Which of the following is correct about $$SL(2,3)$$? - It is a direct product of its 2-Sylow subgroup and 3-Sylow subgroup + It is a semidirect product of its Sylow subgroups, where the 2-Sylow subgroup is the normal piece and the 3-Sylow subgroup is the non-normal piece. - It is a semidirect product of its Sylow subgroups, where the 3-Sylow subgroup is the normal piece and the 2-Sylow subgroup is the non-normal piece. - Neither the 2-Sylow subgroups nor the 3-Sylow subgroups are normal.
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{Which of these groups of order 8 is the 2-Sylow subgroup of $$SL(2,3)$$ isomorphic to? - cyclic group:Z8 - direct product of Z4 and Z2 - dihedral group:D8 + quaternion group - elementary abelian group:E8
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{What is the order of the center of $$SL(2,3)$$? - 1 + 2 - 3 - 4 - 6
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