C₁₇×#2846 #14525852

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁹

Aliases

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

3422 conjugacy classes of subgroups.

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1578);