C₁₇×#12431 #16870175

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12430
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12431

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₂×D₄×C₁₇	D₈
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈×D₄×C₁₇ ◁ G

236 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 2176

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)(20,22)(21,24)(23,25)(26,27,31,35)(28,36,40,52)(29,41,43,56)(30,44,42,34)(32,45,47,38)(33,48,49,37)(39,55,54,51)(46,53,50,57);(26,28,37,53,30,39,43,45,31,40,48,57,42,54,29,38)(27,32,41,51,34,46,49,52,35,47,56,55,44,50,33,36);(19,22)(20,25)(23,24)

Conjugacy classes & character table

833 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5419);