Finite Group Databasebeta

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C7×C25×C22⋊(C13⋊C3) #41031328

order27300
automorphism?
homologyAbelianization (H1) = C3×C7×C25 · Schur multiplier (H2) = C2

Aliases

direct productC7×C25×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C7×C25×C13⋊C3)
unambiguous semidirect productC13⋊(C7×A4×C25)
unambiguous semidirect product(C22×C25)⋊(C7×C13⋊C3)
unambiguous semidirect product(C13×C25)⋊(C7×A4)

Splittings

Fitting, HallC22×C7×C13×C25 ⋊ C3
derived, HallC22×C13 ⋊ C3×C7×C25
HallC7×C13×C25 ⋊ A4
HallC22×C13×C25 ⋊ C3×C7
HallC22×C7×C25 ⋊ C13⋊C3
HallC22×C7×C13 ⋊ C3×C25
HallC13×C25 ⋊ C7×A4
HallC22×C25 ⋊ C7×C13⋊C3
HallC7×C13 ⋊ A4×C25
HallC22×C7 ⋊ C25×C13⋊C3
SylowC13 ⋊ C7×A4×C25
SylowC22 ⋊ C7×C25×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC7×C25C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C3×C7×C25
FrattiniC5C5×C7×C22⋊(C13⋊C3)
FittingC22×C7×C13×C25C3
socleC22×C5×C7×C13C3×C5
prime radicalC5×C7×C22⋊(C13⋊C3)C5
cosocleC22×C5×C13C3×C5×C7
LCSG ▷ C22×C13
UCSC1 ◁ C7×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9100

Conjugacy classes & character table

3500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 218);