C₁₇×C₂²⋊Q₈ #10587648

order	544
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₁₇×C₂²⋊Q₈
unambiguous semidirect product	C₂²⋊(Q₈×C₁₇)

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

74 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 3 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(544, 184);