Finite Group Databasebeta

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C4×C5×C31×C13⋊C3 #37563705

order24180
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C31 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C31×C13⋊C3
unambiguous semidirect product(C4×C13)⋊(C3×C5×C31)
unambiguous semidirect product(C4×C5×C13)⋊(C3×C31)

Splittings

Fitting, HallC4×C5×C13×C31 ⋊ C3
derived, SylowC13 ⋊ C3×C4×C5×C31
HallC5×C13×C31 ⋊ C3×C4
HallC4×C13×C31 ⋊ C3×C5
HallC13×C31 ⋊ C3×C4×C5
HallC4×C5×C13 ⋊ C3×C31
HallC5×C13 ⋊ C3×C4×C31
HallC4×C13 ⋊ C3×C5×C31

Subgroups

subgroupG/H
center, hypercenterC4×C5×C31C13⋊C3
commutator, hypocenterC13C3×C4×C5×C31
FrattiniC2C2×C5×C31×C13⋊C3
FittingC4×C5×C13×C31C3
socleC2×C5×C13×C31C2×C3
prime radicalC2×C5×C31×C13⋊C3C2
cosocleC2×C13C2×C3×C5×C31
LCSG ▷ C13
UCSC1 ◁ C4×C5×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8060

Conjugacy classes & character table

4340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 4);