Finite Group Databasebeta

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C13×C3⋊D345 #41002135

order26910
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C3

Aliases

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

Splittings

Fitting, socle, HallC32×C5×C13×C23 ⋊ C2
derived, HallC32×C5×C23 ⋊ C2×C13
HallC32×C13×C23 ⋊ D5
HallC5×C13×C23 ⋊ C3⋊D3
HallC32×C5×C13 ⋊ D23
HallC13×C23 ⋊ C3⋊D15
HallC32×C23 ⋊ D5×C13
HallC32×C13 ⋊ D115
HallC5×C23 ⋊ C13×C3⋊D3
HallC5×C13 ⋊ C3⋊D69
HallC32×C5 ⋊ C13×D23
SylowC23 ⋊ C13×C3⋊D15
SylowC32 ⋊ C13×D115
SylowC5 ⋊ C13×C3⋊D69

Subgroups

subgroupG/H
center, hypercenterC13C3⋊D345
commutator, cosocle, hypocenterC32×C5×C23C2×C13
FrattiniC1G
Fitting, socleC32×C5×C13×C23C2
LCSG ▷ C32×C5×C23
UCSC1 ◁ C13

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

6747 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 62);