Finite Group Databasebeta

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C23×C3⋊(C5⋊(D13⋊C3)) #41002110

order26910
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C3⋊(C5⋊(D13⋊C3))
unambiguous semidirect productC3⋊(C23×C5⋊(D13⋊C3))
unambiguous semidirect productC5⋊(C23×C3⋊(D13⋊C3))
unambiguous semidirect product(C13⋊C3)⋊(C23×D15)
unambiguous semidirect productD195⋊(C3×C23)
unambiguous semidirect product(C23×D195)⋊C3

Splittings

Fitting, socleC3×C5×C13×C23 ⋊ C2×C3
derivedC3×C5×C13 ⋊ C2×C3×C23
HallC3×C5×C23×C13⋊C3 ⋊ C2
HallC3×C23×C13⋊C3 ⋊ D5
HallC5×C13×C23 ⋊ C3×D3
HallC3×C5×C13⋊C3 ⋊ C2×C23
HallC13×C23 ⋊ C3×D15
HallC3×C13⋊C3 ⋊ D5×C23
HallC5×C23 ⋊ C3⋊(D13⋊C3)
HallC5×C13 ⋊ C3×D3×C23
SylowC13 ⋊ C3×C23×D15
SylowC5 ⋊ C23×C3⋊(D13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC23C3⋊(C5⋊(D13⋊C3))
commutator, cosocle, hypocenterC3×C5×C13C2×C3×C23
FrattiniC1G
Fitting, socleC3×C5×C13×C23C2×C3
LCSG ▷ C3×C5×C13
UCSC1 ◁ C23

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4485

Conjugacy classes & character table

1311 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 37);