C₂²×#511771 #72236278

order	2048
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁸

Aliases

	subgroup	G/H
center, socle	C₂⁴	C₂×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂⁶
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ C₂⁶ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁

823328 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 6 generators on 16 points:

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

260 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((1,2), (3,4), (13,16), (10,13)(14,16), (5,6)(7,8), (6,8)(9,10)(11,13)(12,14)(15,16));