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C3×#66493 #11758291

order984
isoclinismisoclinic class of #4223
automorphism?
homologyAbelianization (H1) = C3×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×#66493

Splittings

derived, SylowC41 ⋊ C3×C8
HallC3×C41 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC2×C3#4223
commutator, hypocenterC41C3×C8
FrattiniC2C3×#4223
Fitting, socle, prime radicalC2×C3×C41C4
cosocleDic41C2×C3
LCSG ▷ C41
UCSC1 ◁ C2×C3

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 984

A minimal faithful permutation representation — 2 generators on 52 points:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10620295, C3⋊#10620295, D3×#66493, …
maximal normal subgroup ofC3×#10620295, C3⋊#10620295, D3×#66493, …
maximal quotient ofC3×#10620270, C2×C3×#66493

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(984, 5);