C₁₇×#7477 #16865221

order	4352
nilpotency class	5
isoclinism	isoclinic class of #1418
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7477

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#357
commutator	C₁₆	C₄²×C₁₇
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₇
prime radical	C₂³×C₁₇	D₁₆
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ C₂²×C₁₆×C₁₇ ◁ G

178 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 102 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 — 2 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)(22,23,26,32)(24,36,38,44)(25,41,43,33)(27,31,45,40)(28,39,46,53)(29,37,30,35)(34,49,51,42)(47,52,48,50);(22,24,27,39,28,40,36,23,30,33,48,34,49,50,43,37,26,38,45,53,46,31,44,32,29,41,47,51,42,52,25,35)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 465);