Finite Group Databasebeta

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C13⋊C3×D345 #41002113

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

Aliases

direct productC13⋊C3×D345
unambiguous semidirect productC3⋊(C13⋊C3×D115)
unambiguous semidirect productC5⋊(C13⋊C3×D69)
unambiguous semidirect productC23⋊(D15×C13⋊C3)
unambiguous semidirect product(C13×D345)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C13×C23 ⋊ C2×C3
HallC3×C5×C23×C13⋊C3 ⋊ C2
HallC3×C23×C13⋊C3 ⋊ D5
HallC5×C13×C23 ⋊ C3×D3
HallC3×C5×C13⋊C3 ⋊ D23
HallC13×C23 ⋊ C3×D15
HallC3×C13⋊C3 ⋊ D115
HallC5×C23 ⋊ D3×C13⋊C3
HallC5×C13 ⋊ C3×D69
SylowC23 ⋊ D15×C13⋊C3
SylowC13 ⋊ C3×D345
SylowC5 ⋊ C13⋊C3×D69

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C13×C23C2×C3
LCSG ▷ C3×C5×C13×C23
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4485

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 40);