C₁₇×#10648 #16868392

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10645
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#10648

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#397
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#126
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

236 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 82 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)(18,19,22,25,23,27,21,26)(20,24,28,33,30,31,29,32)(34,35)(36,44,47,57)(37,41)(38,42)(39,43)(40,46,54,51)(45,60,48,59)(49,55)(50,56)(52,58)(53,62,64,61)(63,65);(18,20)(19,24)(21,29)(22,28)(23,30)(25,33)(26,32)(27,31)(34,36,39,47)(35,40,43,54)(37,48,50,45)(38,51,52,46)(41,53,56,64)(42,57,58,44)(49,61,63,62)(55,60,65,59);(19,25)(20,28)(21,22)(24,31)(26,27)(29,30)(34,37,38,49,39,50,52,63)(35,41,42,55,43,56,58,65)(36,45,46,61,47,48,51,62)(40,53,44,59,54,64,57,60)

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3636);