C₁₇×#10586 #16868330

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#10586

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

350 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 114 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)(18,19,22,24)(20,25,21,23)(26,27,31,35)(28,32,38,41)(29,33,30,34)(36,39,37,40)(42,43)(44,51)(45,49)(46,48)(47,52)(50,54)(53,57)(55,56);(18,20,22,21)(19,23,24,25)(26,28)(27,32)(29,37)(30,36)(31,38)(33,40)(34,39)(35,41)(42,44,45,52)(43,47,49,51)(46,55,54,53)(48,57,50,56);(18,21,22,20)(19,23,24,25)(27,33)(28,36)(29,30)(34,35)(37,38)(39,40)(43,48)(46,54)(47,56)(49,50)(51,57)(53,55)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3574);