C₁₇×#12034 #16869778

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#12034

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
socle	C₂²×C₁₇	C₂×#107
prime radical	C₂³×C₁₇	#107
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 204 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)(18,19,21,24,22,25,28,31)(20,23,27,30,26,29,32,33)(34,35)(36,45)(37,42)(38,52)(39,54)(40,44)(41,48)(43,46)(47,58)(49,64)(50,60)(51,57)(53,65)(55,62)(56,63)(59,61);(18,20)(19,23)(21,27)(22,26)(24,30)(25,29)(28,32)(31,33)(34,36,46,61,39,49,53,63,40,50,51,62,37,47,38,48)(35,41,52,58,42,55,57,60,44,56,65,64,54,59,43,45);(20,26)(23,29)(27,32)(30,33)(34,37,40,39)(35,42,44,54)(36,47,50,49)(38,51,53,46)(41,55,56,59)(43,52,57,65)(45,58,60,64)(48,62,63,61)

Conjugacy classes & character table

986 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5022);