Finite Group Databasebeta

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C2×D13⋊C3×C67⋊C3 #44535694

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

Aliases

direct productC2×D13⋊C3×C67⋊C3
unambiguous semidirect product(C13⋊C3)⋊(C22×C67⋊C3)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C67⋊C3)
unambiguous semidirect product(C2×C67×D13⋊C3)⋊C3
unambiguous semidirect product(C2×#19104948)⋊C3
unambiguous semidirect product(C2×#19104947)⋊C3
unambiguous semidirect product(C2×D13×C67⋊C3)⋊C3

Splittings

Fitting, socleC2×C13×C67 ⋊ C2×C32
derived, HallC13×C67 ⋊ C22×C32
HallC13⋊C3×C67⋊C3 ⋊ C22
HallC2×D13×C67 ⋊ C32
SylowC67 ⋊ C2×C3×D13⋊C3
HallC2×D13 ⋊ C3×C67⋊C3
SylowC13 ⋊ C22×C3×C67⋊C3

Subgroups

subgroupG/H
center, hypercenterC2D13⋊C3×C67⋊C3
commutator, cosocle, hypocenterC13×C67C22×C32
FrattiniC1G
Fitting, socleC2×C13×C67C2×C32
LCSG ▷ C13×C67
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1742

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 130);