C₁₇×#12511 #16870255

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12503
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₇×#12511

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#493	C₂²
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈²×C₁₇ ◁ G

260 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 94 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)(20,26)(21,29)(22,24)(23,27)(25,30)(28,32)(31,33)(34,35)(36,50)(37,43)(38,58)(39,60)(40,48)(41,47)(42,49)(44,55)(45,51)(46,59)(52,62)(53,61)(54,65)(56,63)(57,64);(18,20,21,27,22,28,30,33)(19,23,25,26,24,31,29,32)(34,36,51,56,40,53,59,57,42,55,39,52,41,54,38,37)(35,43,58,65,47,62,60,44,49,64,46,61,48,63,45,50);(19,24)(23,31)(25,29)(26,32)(34,37,38,54,41,52,39,55,42,57,59,53,40,56,51,36)(35,44,45,62,48,65,46,43,49,50,60,63,47,61,58,64)

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5499);