D₄×D₈×C₂₉ #16816993

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

D₄×D₈×C₂₉

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄×D₄×C₂₉ ◁ G

620 conjugacy classes of subgroups.

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2,3,4)(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);(2,4);(5,6,7,8,9,10,11,12);(6,12)(7,11)(8,10)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2011);