C₁₇×#8141 #16865885

order	4352
nilpotency class	2
isoclinism	isoclinic class of #7855
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₇ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₇×#8141

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#376
prime radical	C₂³×C₁₇	#117
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ G

294 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 158 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)(18,19,21,24,22,25,28,31)(20,23,27,30,26,29,32,33)(34,35)(36,44,47,57)(37,41)(38,42)(39,43)(40,46,52,60)(45,56,59,64)(48,53)(49,54)(50,55)(51,58,62,65)(61,63);(18,20)(19,23)(21,27)(22,26)(24,30)(25,29)(28,32)(31,33)(34,36)(35,40,43,52)(37,45)(38,46)(39,47)(41,51,54,62)(42,44,55,57)(48,58)(49,59)(50,60)(53,56,63,64)(61,65);(20,26)(23,29)(27,32)(30,33)(34,37,38,48,39,49,50,61)(35,41,42,53,43,54,55,63)(36,45,46,58,47,59,60,65)(40,51,44,56,52,62,57,64)

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1129);