Finite Group Databasebeta

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C2×C3×C67×D13⋊C3 #44535750

order31356
automorphism?
homologyAbelianization (H1) = C22×C32×C67 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C67×D13⋊C3
unambiguous semidirect productD13⋊(C2×C32×C67)
unambiguous semidirect product(C13⋊C3)⋊(C22×C3×C67)
unambiguous semidirect product(C2×D13)⋊(C32×C67)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C3×C67)
unambiguous semidirect product(C2×C3×D13)⋊(C3×C67)

Splittings

Fitting, socleC2×C3×C13×C67 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C32×C67
HallC3×C13⋊C3×C67 ⋊ C22
HallC2×D13×C67 ⋊ C32
HallC13×C67 ⋊ C22×C32
HallC3×C13⋊C3 ⋊ C22×C67
HallC2×D13 ⋊ C32×C67

Subgroups

subgroupG/H
center, hypercenterC2×C3×C67D13⋊C3
commutator, cosocle, hypocenterC13C22×C32×C67
FrattiniC1G
Fitting, socleC2×C3×C13×C67C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C3×C67

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5226

Conjugacy classes & character table

3216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 186);