C₂×D₄×D₈×C₁₇ #16918783

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₇ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂×D₄×D₈×C₁₇

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄×D₄×C₁₇ ◁ G

3710 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 5 generators on 31 points:

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

1190 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 54027);