C₁₇×#466 #11762407

order	1088
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

134 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 544

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1088, 147);