C₁₇×#11970 #16869714

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11858
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#11970

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 ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 284 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)(18,19,21,25,22,24,30,32)(20,26,27,33,28,23,29,31)(34,35,39,45,40,43,55,61,41,46,53,63,37,52,38,44)(36,47,50,60,48,62,49,57,51,64,54,42,56,58,65,59);(18,20,22,28)(19,23,24,26)(21,29,30,27)(25,33,32,31)(34,36)(35,42)(37,48)(38,54)(39,49)(40,56)(41,51)(43,57)(44,62)(45,47)(46,60)(50,55)(52,59)(53,65)(58,61)(63,64);(19,24)(23,26)(25,32)(31,33)(34,37,41,40)(35,43,46,52)(36,48,51,56)(38,53,55,39)(42,57,60,59)(44,45,61,63)(47,58,64,62)(49,54,65,50)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4958);