C₁₇×#13413 #16871157

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13331
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13413

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#459
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₂×C₁₇×#493	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

540 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 37
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23)(24,31)(25,26)(27,30)(28,32)(29,35)(33,34);(23,26)(24,32)(25,35)(28,34)(29,30)(31,36)(33,37);(19,21)(22,24,25,33,27,34,35,31)(23,28,29,37,30,32,26,36)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6401);