Finite Group Databasebeta

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C25×C31×C13⋊C3 #44475221

order30225
automorphism?
homologyAbelianization (H1) = C3×C25×C31 · Schur multiplier (H2) = C1

Aliases

direct productC25×C31×C13⋊C3
unambiguous semidirect productC13⋊(C3×C25×C31)
unambiguous semidirect product(C13×C25)⋊(C3×C31)

Splittings

Fitting, HallC13×C25×C31 ⋊ C3
derived, SylowC13 ⋊ C3×C25×C31
HallC13×C31 ⋊ C3×C25
HallC13×C25 ⋊ C3×C31

Subgroups

subgroupG/H
center, hypercenterC25×C31C13⋊C3
commutator, hypocenterC13C3×C25×C31
FrattiniC5C5×C31×C13⋊C3
FittingC13×C25×C31C3
socleC5×C13×C31C3×C5
prime radicalC5×C31×C13⋊C3C5
cosocleC5×C13C3×C5×C31
LCSG ▷ C13
UCSC1 ◁ C25×C31

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10075

Conjugacy classes & character table

5425 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30225, 4);