Finite Group Databasebeta

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C3×Dic82 #11758301

order984
isoclinismisoclinic class of Dic82
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic82
unambiguous semidirect productC41⋊(C3×Q8)

Splittings

HallC3×C41 ⋊ Q8
SylowC41 ⋊ C3×Q8

Subgroups

subgroupG/H
centerC2×C3C2×D41
commutator, cosocleC2×C41C22×C3
FrattiniC2C2×C3×D41
FittingC3×C4×C41C2
socle, prime radicalC2×C3×C41C22
hypercenterC3×C4D41
hypocenterC41C3×Q8
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C2×C3 ◁ C3×C4

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

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14520094, #14520096, #14520099, …
maximal normal subgroup of#14520094, #14520096, #14520099, …
maximal quotient ofC3×#10620279, C3×C4⋊Dic41, C2×C3×Dic82

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(984, 15);