C₁₇×#13450 #16871194

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13450

Subgroups

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

410 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 130 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)(20,21)(26,27,34,41)(28,42,47,57)(29,48,45,55)(30,38,49,39)(31,37,32,52)(33,53,43,40)(35,51,56,44)(36,50,54,46);(22,23)(24,25)(26,28,34,47)(27,35,41,56)(29,49,45,30)(31,44,32,51)(33,50,43,46)(36,37,54,52)(38,42,39,57)(40,48,53,55);(19,21)(23,25)(26,29,30,28,43,44,32,50,34,45,49,47,33,51,31,46)(27,36,37,56,53,57,39,55,41,54,52,35,40,42,38,48)

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, 6438);