Finite Group Databasebeta

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C2×C7×C25⋊(D13⋊C3) #41031248

order27300
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C25⋊(D13⋊C3)
unambiguous semidirect product(C2×C25)⋊(C7×D13⋊C3)
unambiguous semidirect product(C2×C13⋊C3)⋊(C7×D25)
unambiguous semidirect product(C2×D325)⋊(C3×C7)

Splittings

FittingC2×C7×C13×C25 ⋊ C2×C3
derived, HallC13×C25 ⋊ C22×C3×C7
HallC2×C7×D325 ⋊ C3
HallC7×C25×C13⋊C3 ⋊ C22
HallC7×C13×C25 ⋊ C22×C3
HallC2×D325 ⋊ C3×C7
HallC25×C13⋊C3 ⋊ C22×C7
HallC7×C13⋊C3 ⋊ C2×D25
HallC7×C25 ⋊ C2×D13⋊C3
HallC7×C13 ⋊ C2×C3×D25
HallC13⋊C3 ⋊ C2×C7×D25
SylowC25 ⋊ C2×C7×D13⋊C3
SylowC13 ⋊ C2×C3×C7×D25

Subgroups

subgroupG/H
center, hypercenterC2×C7C25⋊(D13⋊C3)
commutator, cosocle, hypocenterC13×C25C22×C3×C7
FrattiniC5C2×C7×C5⋊(D13⋊C3)
FittingC2×C7×C13×C25C2×C3
socleC2×C5×C7×C13C3×D5
LCSG ▷ C13×C25
UCSC1 ◁ C2×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4550

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 138);