C₂×C₁₇×#3264 #16918766

order	4352
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₇ · Schur multiplier (H₂) = C₂⁹

Aliases

	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

3366 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)(8,11)(9,14)(12,13);(7,8)(9,12)(10,13)(11,14);(4,6);(8,12)(9,14)(11,13)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 54010);