C₁₇×#10084 #16867828

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

Aliases

direct product

C₁₇×#10084

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

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

normal subgroups only

This group has 484 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) = 53
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 3 generators on 53 points:

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

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, 3072);