C₂⁴×D₄×C₂₉ #16817302

order	3712
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₂₉ · Schur multiplier (H₂) = C₂¹⁵

Aliases

direct product	C₂⁴×D₄×C₂₉
unambiguous semidirect product	C₄⋊(C₂⁵×C₂₉)
unambiguous semidirect product	C₂²⋊(C₂⁵×C₂₉)

	subgroup	G/H
center, socle	C₂⁵×C₂₉	C₂²
commutator, Frattini, cosocle	C₂	C₂⁶×C₂₉
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₂₉ ◁ G

10552 conjugacy classes of subgroups.

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 6 generators on 41 points:

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

2320 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2320);