C₁₇×#2867 #14525873

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³×C₄³

Aliases

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

1272 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1088

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1599);