C₁₇×#8788 #16866532

order	4352
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#8788

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle, prime radical	C₂³×C₁₇	C₂×C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ C₄³×C₁₇ ◁ G

322 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 57
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 3 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27)(28,36)(29,32)(30,40)(31,35)(33,38)(34,37)(39,41)(42,43,45,48,46,49,52,55)(44,47,51,54,50,53,56,57);(19,22)(23,25)(26,28,37,39,31,38,30,29)(27,32,40,33,35,41,34,36)(42,44)(43,47)(45,51)(46,50)(48,54)(49,53)(52,56)(55,57);(18,20,21,24)(19,23,22,25)(26,29,30,38,31,39,37,28)(27,33,34,32,35,36,40,41)(44,50)(47,53)(51,56)(54,57)

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1776);