C₁₇×#24412 #16882156

order	4352
nilpotency class	3
isoclinism	isoclinic class of #24412
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

1710 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 17400);