C₁₇×#13415 #16871159

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

Aliases

direct product

C₁₇×#13415

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#459
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₂³×C₁₇	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 436 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) = 53
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,29,35)(24,27,38,45)(25,36,42,52)(26,34,28,32)(30,33,43,37)(31,47,49,41)(39,44,48,53)(40,50,46,51);(22,24,29,38)(23,30,35,43)(25,39,42,48)(26,33,28,37)(27,32,45,34)(31,40,49,46)(36,47,52,41)(44,51,53,50);(19,21)(22,25,26,40,29,42,28,46)(23,31,32,48,35,49,34,39)(24,36,37,51,38,52,33,50)(27,44,43,41,45,53,30,47)

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, 6403);