Finite Group Databasebeta

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C5×C3⋊(C23⋊(D13⋊C3)) #41002107

order26910
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(C23⋊(D13⋊C3))
unambiguous semidirect productC3⋊(C5×C23⋊(D13⋊C3))
unambiguous semidirect productC23⋊(C5×C3⋊(D13⋊C3))
unambiguous semidirect product(C13⋊C3)⋊(C5×D69)
unambiguous semidirect productD897⋊(C3×C5)
unambiguous semidirect product(C5×D897)⋊C3

Splittings

Fitting, socleC3×C5×C13×C23 ⋊ C2×C3
derivedC3×C13×C23 ⋊ C2×C3×C5
HallC3×C5×C23×C13⋊C3 ⋊ C2
HallC3×C23×C13⋊C3 ⋊ C2×C5
HallC5×C13×C23 ⋊ C3×D3
HallC3×C5×C13⋊C3 ⋊ D23
HallC13×C23 ⋊ C3×C5×D3
HallC3×C13⋊C3 ⋊ C5×D23
HallC5×C23 ⋊ C3⋊(D13⋊C3)
HallC5×C13 ⋊ C3×D69
SylowC23 ⋊ C5×C3⋊(D13⋊C3)
SylowC13 ⋊ C3×C5×D69

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C23⋊(D13⋊C3))
commutator, cosocle, hypocenterC3×C13×C23C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C23C2×C3
LCSG ▷ C3×C13×C23
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4485

Conjugacy classes & character table

1230 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 34);