Finite Group Databasebeta

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C7×A4×C13×C25 #41031327

order27300
automorphism?
homologyAbelianization (H1) = C3×C7×C13×C25 · Schur multiplier (H2) = C2

Aliases

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

Splittings

Fitting, HallC22×C7×C13×C25 ⋊ C3
derived, SylowC22 ⋊ C3×C7×C13×C25
HallC22×C13×C25 ⋊ C3×C7
HallC22×C7×C25 ⋊ C3×C13
HallC22×C7×C13 ⋊ C3×C25
HallC22×C25 ⋊ C3×C7×C13
HallC22×C13 ⋊ C3×C7×C25
HallC22×C7 ⋊ C3×C13×C25

Subgroups

subgroupG/H
center, hypercenterC7×C13×C25A4
commutator, hypocenterC22C3×C7×C13×C25
FrattiniC5C5×C7×A4×C13
FittingC22×C7×C13×C25C3
socleC22×C5×C7×C13C3×C5
prime radicalC5×C7×A4×C13C5
cosocleC22×C5C3×C5×C7×C13
LCSG ▷ C22
UCSC1 ◁ C7×C13×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9100

Conjugacy classes & character table

9100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 217);