C₂³×#41×C₁₉ #14561447

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₉ · Schur multiplier (H₂) = C₂¹⁴

Aliases

C₂³×#41×C₁₉

	subgroup	G/H
center	C₂³×C₄×C₁₉	C₂²
commutator, Frattini, cosocle	C₂	C₂⁶×C₁₉
socle	C₂⁴×C₁₉	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₉ ◁ G

6520 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 6 generators on 33 points:

(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(3,4);(5,6);(7,8)(9,12)(10,11)(13,14);(8,11)(12,14);(7,9,10,13)(8,12,11,14)

1520 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2322);