C₁₇×#8792 #16866536

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8790
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₇×#8792

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#382
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#124
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

262 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 126 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)(20,25)(21,30)(22,32)(23,27)(24,28)(26,31)(29,33)(34,35)(36,44,47,40)(37,48,50,63)(38,43)(39,42)(41,49,54,64)(45,58)(46,57,61,53)(51,55)(52,59)(56,65)(60,62);(18,20,22,28,23,29,31,21)(19,24,26,25,27,30,32,33)(34,36,38,46,39,47,51,61)(35,40,43,53,42,44,55,57)(37,45,49,59,50,60,64,65)(41,52,48,62,54,56,63,58);(18,21,31,29,23,28,22,20)(19,25,32,24,27,33,26,30)(34,37,39,50)(35,41)(36,45,47,60)(38,49,51,64)(40,52)(42,54)(43,48)(44,56)(46,59,61,65)(53,62)(55,63)(57,58)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1780);