Finite Group Databasebeta

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C3×(C49⋊C3)⋊#261 #37524192

order22932
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C49⋊C3)⋊#261
unambiguous semidirect product(C49⋊C3)⋊(C3×#261)

Splittings

FittingC3×C13×C49 ⋊ C3×C4
derived, HallC13×C49 ⋊ C32×C4
HallC3×C13×C49⋊C3 ⋊ C4
HallC49⋊#261 ⋊ C32
HallC3×C49⋊C3 ⋊ #261
SylowC49 ⋊ C32×#261
SylowC13 ⋊ C3×(C49⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC3(C49⋊C3)⋊#261
commutator, hypocenterC13×C49C32×C4
FrattiniC7C3×ΓL(1,𝔽8)⋊#261
FittingC3×C13×C49C3×C4
socleC3×C7×C13ΓL(1,𝔽8)⋊C4
prime radicalC3×D13×C49⋊C3C2
cosocleD13×C49C2×C32
LCSG ▷ C13×C49
UCSC1 ◁ C3

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1911

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 137);