C₂³×D₈×C₁₉ #14561431

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₉ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂³×D₈×C₁₉

	subgroup	G/H
center, socle	C₂⁴×C₁₉	D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₁₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

1976 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 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);(7,8,9,10,11,12,13,14);(8,14)(9,13)(10,12)

1064 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2306);