C₁₇×#10630 #16868374

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10370
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#10630

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#124
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#397
prime radical	C₂³×C₁₇	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 1088

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

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3618);