Finite Group Databasebeta

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C3×C3⋊(Dic131⋊C5) #37556066

order23580
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(Dic131⋊C5)
unambiguous semidirect productC3⋊(C3×Dic131⋊C5)
unambiguous semidirect product(C131⋊C5)⋊(C3×Dic3)
unambiguous semidirect productDic393⋊(C3×C5)
unambiguous semidirect product(C3×Dic393)⋊C5

Splittings

derivedC3×C131 ⋊ C3×C4×C5
HallC32×C131⋊C5 ⋊ C4
HallC3×Dic393 ⋊ C5
HallC32×C131 ⋊ C4×C5
HallC131⋊C5 ⋊ C3×Dic3
SylowC131 ⋊ C3×C5×Dic3
SylowC32 ⋊ Dic131⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(D131⋊C5)
commutator, hypocenterC3×C131C3×C4×C5
FrattiniC2C3×C3⋊(D131⋊C5)
Fitting, socleC2×C32×C131C2×C5
prime radicalC2×C32×C131⋊C5C2
cosocleC2×C3×C131C2×C3×C5
LCSG ▷ C3×C131
UCSC1 ◁ C2×C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1572

Conjugacy classes & character table

324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23580, 41);