C₁₇×#7363 #16865107

order	4352
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7363

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₇	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₁₆×C₁₇
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₇
socle	C₂²×C₁₇	C₂²⋊C₁₆
prime radical	C₂³×C₁₇	M₃₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇ ◁ C₂²×C₁₆×C₁₇ ◁ G

124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 89
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 2 generators on 89 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24,25,22)(21,23)(26,27,30,36,31,37,49,62,32,38,50,63,52,65,77,85,33,39,51,64,53,66,78,86,29,35,46,59,47,60,74,83)(28,40,42,67,43,68,71,87,41,57,69,61,70,81,88,84,44,58,48,75,72,82,76,89,45,34,54,55,73,56,79,80);(18,20,21,25)(19,22,23,24)(26,28)(27,34)(29,45)(30,48)(31,43)(32,41)(33,44)(35,58)(36,61)(37,56)(38,40)(39,57)(42,51)(46,69)(47,73)(49,76)(50,54)(52,70)(53,72)(55,64)(59,67)(60,82)(62,84)(63,75)(65,68)(66,81)(71,78)(74,88)(77,79)(80,86)(83,87)(85,89)

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 351);