C₁₇×#7474 #16865218

order	4352
nilpotency class	5
isoclinism	isoclinic class of #1426
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7474

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#367
commutator	C₁₆	C₄²×C₁₇
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₇
prime radical	C₂³×C₁₇	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ C₂²×C₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 174 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)(23,29,30,45)(24,34)(25,39)(26,42)(27,36)(31,50,49,32)(33,53,46,48)(35,43)(37,41)(38,40)(44,51,52,47);(19,21)(22,23,25,31,26,32,24,29,36,46,34,47,35,44,39,53,28,30,41,49,43,50,38,45,27,33,40,51,42,52,37,48)

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, 462);