C₁₇×#1999 #14525005

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

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

496 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(26,27)(28,30)(29,32)(31,33);(22,23)(24,25)(27,30)(28,33)(31,32);(19,21)(23,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 731);