C₂³×#2403 #72233014

order	1024
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁷ · Schur multiplier (H₂) = C₂²³

Aliases

	subgroup	G/H
center, socle	C₂⁶	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁷
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁶ ◁ G
LECS	G ▷ C₂³ ▷ C₁

805045 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 7 generators on 18 points:

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

304 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((3,4), (5,6), (1,2)(3,4)(5,6), (8,10)(12,14)(16,18), (16,18), (11,12)(13,14)(15,16)(17,18), (7,8)(9,10)(11,12)(13,14));