Groups of order 3.5.2^n

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This article discusses the groups of order 3 \cdot 5 \cdot 2^n = 15 \cdot 2^n, where n varies over nonnegative integers.

Number of groups of small orders

Exponent n Value 2^n Value 3 \cdot 5 \cdot 2^n Number of groups of order 3 \cdot 5 \cdot 2^n Reason/explanation/list
0 1 15 1 See classification of groups of order a product of two distinct primes
1 2 30 4 See groups of order 30.
2 4 60 13 See groups of order 60. This is the smallest order for which we have a non-solvable group, namely alternating group:A5. See A5 is the simple non-abelian group of smallest order.
3 8 120 47 See groups of order 120.
4 16 240 208 See groups of order 240.
5 32 480 1213 See groups of order 480.
6 64 960 11394 See groups of order 960.
7 128 1920 241004 See groups of order 1920.