C₁₇×#11669 #16869413

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11669
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#11669

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#418
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
socle	C₂×C₁₇	#1490
prime radical	C₁₇×#575	C₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₄×M₁₆×C₁₇ ◁ G

360 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 272

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)(18,19,21,28,24,29,33,27,25,30,22,32,23,20,31,26);(18,20)(19,24)(21,26)(22,27)(23,30)(25,29)(28,33)(31,32);(18,21,23,31,25,22,24,33)(19,26,29,28,30,27,20,32)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4657);