C₁₇×#12294 #16870038

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12108
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12294

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₁₇×#3259	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#424 ◁ G

302 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 74 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)(18,19,22,25)(20,23,27,30)(21,24,28,31)(26,32,33,29)(34,35,40,46)(36,47,50,62)(37,41,54,58)(38,45,39,44)(42,55,60,49)(43,53,57,51)(48,61,52,59)(56,64,63,65);(18,20)(19,23)(21,26)(22,27)(24,29)(25,30)(28,33)(31,32)(35,41)(37,51)(38,39)(42,56)(43,45)(44,57)(46,58)(47,61)(48,64)(49,55)(52,65)(53,54)(59,62)(60,63);(18,21,22,28)(19,24,25,31)(20,26,27,33)(23,29,30,32)(34,36,40,50)(35,42,46,60)(37,52,54,48)(38,55,39,49)(41,56,58,63)(43,61,57,59)(44,62,45,47)(51,65,53,64)

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5282);