C₁₇×#123 #10587649

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

Aliases

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

78 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)(23,26)(24,28);(22,23)(24,27)(25,26)(28,29);(18,19)(20,21)(22,24,25,28)(23,27,26,29)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(544, 185);