C₁₇×#9422 #16867166

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9415
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9422

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#123
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 384 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)(18,19,24,27,23,20,22,26)(21,25,31,33,30,28,29,32)(34,35)(36,45)(37,49,52,59)(38,53)(39,43)(40,44)(41,47)(42,51,58,50)(46,61,63,55)(48,56)(54,57)(60,62,65,64);(18,20,23,19)(21,28,30,25)(22,26,24,27)(29,32,31,33)(34,36,38,47,40,48,39,54)(35,41,43,45,44,57,53,56)(37,46,51,64,52,63,50,62)(42,55,59,60,58,61,49,65);(18,21,23,30)(19,25,20,28)(22,31,24,29)(26,33,27,32)(34,37)(35,42)(36,46)(38,51)(39,50)(40,52)(41,55)(43,59)(44,58)(45,60)(47,64)(48,63)(49,53)(54,62)(56,65)(57,61)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 2410);