C₂×C₅×Q₈×C₁₇ #13062850

order	1360
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

C₂×C₅×Q₈×C₁₇

	subgroup	G/H
center, socle, prime radical	C₂²×C₅×C₁₇	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₅×C₁₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅×C₁₇ ◁ G

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 1360

A minimal faithful permutation representation — 3 generators on 32 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 218);