Finite Group Databasebeta

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C2×C3×C13×D67⋊C3 #44535749

order31356
automorphism?
homologyAbelianization (H1) = C22×C32×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C13×D67⋊C3
unambiguous semidirect productD67⋊(C2×C32×C13)
unambiguous semidirect product(C67⋊C3)⋊(C22×C3×C13)
unambiguous semidirect product(C2×D67)⋊(C32×C13)
unambiguous semidirect product(C2×C67⋊C3)⋊(C2×C3×C13)
unambiguous semidirect product(C2×C3×D67)⋊(C3×C13)

Splittings

Fitting, socleC2×C3×C13×C67 ⋊ C2×C3
derived, SylowC67 ⋊ C22×C32×C13
HallC3×C13×C67⋊C3 ⋊ C22
HallC2×C13×D67 ⋊ C32
HallC13×C67 ⋊ C22×C32
HallC3×C67⋊C3 ⋊ C22×C13
HallC2×D67 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13D67⋊C3
commutator, cosocle, hypocenterC67C22×C32×C13
FrattiniC1G
Fitting, socleC2×C3×C13×C67C2×C3
LCSG ▷ C67
UCSC1 ◁ C2×C3×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5226

Conjugacy classes & character table

1326 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 185);