Finite Group Databasebeta

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C2×C13×D223⋊C3 #46852280

order34788
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D223⋊C3
unambiguous semidirect productD223⋊(C2×C3×C13)
unambiguous semidirect product(C223⋊C3)⋊(C22×C13)
unambiguous semidirect product(C2×D223)⋊(C3×C13)
unambiguous semidirect product(C2×C223⋊C3)⋊(C2×C13)

Splittings

Fitting, socleC2×C13×C223 ⋊ C2×C3
derived, SylowC223 ⋊ C22×C3×C13
HallC2×C13×D223 ⋊ C3
HallC13×C223⋊C3 ⋊ C22
HallC13×C223 ⋊ C22×C3
HallC2×D223 ⋊ C3×C13
HallC223⋊C3 ⋊ C22×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D223⋊C3
commutator, cosocle, hypocenterC223C22×C3×C13
FrattiniC1G
Fitting, socleC2×C13×C223C2×C3
LCSG ▷ C223
UCSC1 ◁ C2×C13

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5798

Conjugacy classes & character table

1118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34788, 38);