C₂³×D₈×C₂₉ #16817288

order	3712
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂³×D₈×C₂₉

	subgroup	G/H
center, socle	C₂⁴×C₂₉	D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₂₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

1976 conjugacy classes of subgroups.

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 5 generators on 43 points:

(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(3,4);(5,6);(7,8,9,10,11,12,13,14);(8,14)(9,13)(10,12)

1624 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2306);