Groups of order 2^3.3^n

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This article discusses the groups of order 2^3 \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 2^3 = 8, which must be one of the groups of order 8.

See also groups of order 3^n, groups of order 2.3^n, groups of order 2^2.3^n.

Number of groups of small orders

Exponent n Value 3^n Value 2 \cdot 3^n Number of groups of order 2 \cdot 3^n Reason/explanation/list
0 1 8 5 See groups of order 8, classification of groups of prime-cube order
1 3 24 15 See groups of order 24.
2 9 72 50 See groups of order 72.
3 27 216 177 See groups of order 216.
4 81 648 757 See groups of order 648.
5 243 1944 3973 See groups of order 1944.