Groups of order 2^2.3^n

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This article discusses the groups of order 2^2 \cdot 3^n, where n varies over nonnegative integers. Note that any such group has a 3-Sylow subgroup of order 3^n and a 2-Sylow subgroup of order 2^2 = 4.

See also groups of order 3^n and groups of order 2.3^n.

Number of groups of small orders

Exponent n Value 3^n Value 2^2 \cdot 3^n Number of groups of order 2^2 \cdot 3^n Reason/explanation/list
0 1 4 2 See groups of order 4 and classification of groups of prime-square order. The groups are cyclic group:Z4 and Klein four-group.
1 3 12 5 See groups of order 12.
2 9 36 14 See groups of order 36.
3 27 108 45 See groups of order 108.
4 81 324 176 See groups of order 324.
5 243 972 900 See groups of order 972.