C₂×C₁₇×#532 #14526448

order	2176
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₇ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×C₁₇×#532

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₇
socle	C₂³×C₁₇	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ G

1728 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);(4,6)(7,8)(9,12)(10,11)(13,14);(8,11)(12,14);(3,4,5,6);(7,9,10,13)(8,12,11,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2174);