C₁₇×#8463 #16866207

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8453
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#8463

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₁₇×#3493	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

718 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 142 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)(20,26,28,23)(21,24)(22,25)(27,32,33,30)(29,31)(34,35,39,44,40,45,38,43)(36,46,50,41,49,56,48,55)(37,42,51,57,52,58,53,59)(47,61,62,65,63,60,64,54);(18,20)(19,23)(21,27)(22,28)(24,30)(25,26)(29,33)(31,32)(34,36)(35,41)(37,47)(38,50)(39,48)(40,49)(42,54)(43,56)(44,46)(45,55)(51,64)(52,63)(53,62)(57,60)(58,65)(59,61);(18,21,22,29)(19,24,25,31)(20,27,28,33)(23,30,26,32)(34,37)(35,42)(36,47)(38,53)(39,51)(40,52)(41,54)(43,59)(44,57)(45,58)(46,60)(48,64)(49,63)(50,62)(55,65)(56,61)

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, 1451);