C₂²×#8453 #72275361

order	1024
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹²

Aliases

45229 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 5 generators on 20 points:

(5,6,7,9)(8,11,12,10)(14,17,18,19);(1,2);(5,6)(7,10)(8,11)(9,12)(13,14,16,18)(15,19,20,17);(3,4);(15,20)(17,19)

maximal subgroup of	C₂²×#144364, C₂²×#133839, C₂²×#144366, …
maximal normal subgroup of	C₂²×#144364, C₂²×#133839, C₂²×#144366, …

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((5,6,7,9)(8,11,12,10)(14,17,18,19), (1,2), (5,6)(7,10)(8,11)(9,12)(13,14,16,18)(15,19,20,17), (3,4), (15,20)(17,19));