Finite Group Databasebeta

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C3×C5×C13×D69 #41002123

order26910
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C13×D69
unambiguous semidirect productC3⋊(C3×C5×C13×D23)
unambiguous semidirect productC23⋊(C3×C5×D3×C13)

Splittings

Fitting, socle, HallC32×C5×C13×C23 ⋊ C2
derivedC3×C23 ⋊ C2×C3×C5×C13
HallC32×C13×C23 ⋊ C2×C5
HallC5×C13×C23 ⋊ C3×D3
HallC32×C5×C23 ⋊ C2×C13
HallC32×C5×C13 ⋊ D23
HallC13×C23 ⋊ C3×C5×D3
HallC32×C23 ⋊ C2×C5×C13
HallC32×C13 ⋊ C5×D23
HallC5×C23 ⋊ C3×D3×C13
HallC32×C5 ⋊ C13×D23
SylowC23 ⋊ C3×C5×D3×C13
SylowC32 ⋊ C5×C13×D23

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13D69
commutator, cosocle, hypocenterC3×C23C2×C3×C5×C13
FrattiniC1G
Fitting, socleC32×C5×C13×C23C2
LCSG ▷ C3×C23
UCSC1 ◁ C3×C5×C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8970

Conjugacy classes & character table

7020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 50);