Finite Group Databasebeta

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C2×C7×C25×D13⋊C3 #41031236

order27300
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C25×D13⋊C3
unambiguous semidirect productD13⋊(C2×C3×C7×C25)
unambiguous semidirect product(C13⋊C3)⋊(C22×C7×C25)
unambiguous semidirect product(C2×D13)⋊(C3×C7×C25)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C7×C25)
unambiguous semidirect product(C2×C25×D13)⋊(C3×C7)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C7×C25D13⋊C3
commutator, hypocenterC13C22×C3×C7×C25
FrattiniC5C2×C5×C7×D13⋊C3
FittingC2×C7×C13×C25C2×C3
socleC2×C5×C7×C13C2×C3×C5
prime radicalC2×C5×C7×D13⋊C3C5
cosocleC5×C13C22×C3×C5×C7
LCSG ▷ C13
UCSC1 ◁ C2×C7×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4550

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 126);