C₂⁴×#407 #72302899

order	1024
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₄ · Schur multiplier (H₂) = C₂²¹

Aliases

C₂⁴×#407

484085 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 7 generators on 20 points:

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

448 conjugacy classes. The character table is too large to display.

maximal subgroup of	C₂×#72235589, C₂⁴×#2010, C₂×#72236790
maximal normal subgroup of	C₂×#72235589, C₂⁴×#2010, C₂×#72236790

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

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