C₁₇×#12412 #16870156

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12324
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12412

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₂×D₈×C₁₇	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#446 ◁ G

280 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 82 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)(18,19,24,28)(20,29,21,32)(22,27,23,26)(25,31,33,30)(34,35,40,44)(36,45,48,63)(37,42,39,54)(38,50,53,61)(41,56,58,47)(43,49,62,52)(46,64,55,60)(51,57,65,59);(18,20,24,21)(19,25,28,33)(22,31,23,30)(26,32,27,29)(34,36,40,48)(35,41,44,58)(37,46,39,55)(38,51,53,65)(42,57,54,59)(43,60,62,64)(45,61,63,50)(47,49,56,52);(18,21,24,20)(19,25,28,33)(22,30,23,31)(26,32,27,29)(34,37,40,39)(35,42,44,54)(36,46,48,55)(38,52,53,49)(41,57,58,59)(43,61,62,50)(45,60,63,64)(47,65,56,51)

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, 5400);