C₁₇×#12502 #16870246

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12483
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#12502

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈²×C₁₇ ◁ G

200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 4352

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

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5490);