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C3×D164 #11758303

order984
isoclinismisoclinic class of Dic82
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D164
unambiguous semidirect productC4⋊(C3×D41)

Splittings

FittingC3×C4×C41 ⋊ C2
HallC3×C41 ⋊ D4
SylowC41 ⋊ C3×D4

Subgroups

subgroupG/H
centerC2×C3C2×D41
commutator, cosocleC2×C41C22×C3
FrattiniC2C2×C3×D41
FittingC3×C4×C41C2
socleC2×C3×C41C22
hypercenterC3×C4D41
hypocenterC41C3×D4
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C2×C3 ◁ C3×C4

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 492

A minimal faithful permutation representation — 2 generators on 48 points:

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

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14520090, #14520091, #14520093, …
maximal normal subgroup of#14520090, #14520091, #14520093, …
maximal quotient ofC3×#10620273, C3×D328, C3×Dic164, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(984, 17);