Finite Group Databasebeta

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C3×C13⋊C3×D115 #41002105

order26910
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C13⋊C3×D115
unambiguous semidirect productC5⋊(C3×C13⋊C3×D23)
unambiguous semidirect productC23⋊(C3×D5×C13⋊C3)
unambiguous semidirect product(C13×D115)⋊C32
unambiguous semidirect product(C3×C13×D115)⋊C3

Splittings

Fitting, socleC3×C5×C13×C23 ⋊ C2×C3
derived, HallC5×C13×C23 ⋊ C2×C32
HallC3×C5×C23×C13⋊C3 ⋊ C2
HallC13×D115 ⋊ C32
HallC3×C23×C13⋊C3 ⋊ D5
HallC3×C5×C13⋊C3 ⋊ D23
HallC13×C23 ⋊ C32×D5
HallC5×C23 ⋊ C2×C3×C13⋊C3
HallC5×C13 ⋊ C32×D23
SylowC23 ⋊ C3×D5×C13⋊C3
SylowC13 ⋊ C32×D115
SylowC5 ⋊ C3×C13⋊C3×D23

Subgroups

subgroupG/H
center, hypercenterC3C13⋊C3×D115
commutator, cosocle, hypocenterC5×C13×C23C2×C32
FrattiniC1G
Fitting, socleC3×C5×C13×C23C2×C3
LCSG ▷ C5×C13×C23
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4485

Conjugacy classes & character table

1239 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 32);