Finite Group Databasebeta

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C4×C5×C313⋊C3 #34037419

order18780
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C313⋊C3
unambiguous semidirect product(C4×C313)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C313)⋊C3

Splittings

Fitting, HallC4×C5×C313 ⋊ C3
derived, SylowC313 ⋊ C3×C4×C5
HallC5×C313 ⋊ C3×C4
HallC4×C313 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5C313⋊C3
commutator, hypocenterC313C3×C4×C5
FrattiniC2C2×C5×C313⋊C3
FittingC4×C5×C313C3
socleC2×C5×C313C2×C3
prime radicalC2×C5×C313⋊C3C2
cosocleC2×C313C2×C3×C5
LCSG ▷ C313
UCSC1 ◁ C4×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6260

Conjugacy classes & character table

2140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18780, 2);