C₁₇×#11653 #16869397

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11651
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#11653

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₂³×C₁₇	#102
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

300 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 65
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 65 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,24,22,25,28,31)(20,23,27,30,26,29,32,33)(34,35)(36,45,48,62)(37,41)(38,52)(39,44)(40,47,56,63)(42,50)(43,51)(46,61,49,58)(53,60,64,55)(54,57)(59,65);(18,20)(19,23)(21,27)(22,26)(24,30)(25,29)(28,32)(31,33)(34,36,39,48)(35,40,44,56)(37,46,51,49)(38,53,54,64)(41,55,43,60)(42,58,59,61)(45,52,62,57)(47,50,63,65);(20,26)(23,29)(27,32)(30,33)(34,37,39,51)(35,41,44,43)(36,46,48,49)(38,50,54,65)(40,55,56,60)(42,57,59,52)(45,61,62,58)(47,53,63,64)

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, 4641);