C₂²×D₄×#2846 #72289554

order	4096
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁸ · Schur multiplier (H₂) = C₂³¹

Aliases

C₂²×D₄×#2846

	subgroup	G/H
center, socle	C₂⁶	C₂⁶
commutator, Frattini, cosocle	C₂⁴	C₂⁸
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁶ ◁ G
LECS	G ▷ C₂⁴ ▷ C₁

230519515 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 8 generators on 20 points:

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

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

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

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