Finite Group Databasebeta

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C2×C112×D13⋊C3 #34038420

order18876
automorphism?
homologyAbelianization (H1) = C22×C3×C112 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C112×D13⋊C3
unambiguous semidirect productD13⋊(C2×C3×C112)
unambiguous semidirect product(C13⋊C3)⋊(C22×C112)
unambiguous semidirect product(C2×D13)⋊(C3×C112)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C112)
unambiguous semidirect product(C2×C11×D13)⋊(C3×C11)

Splittings

Fitting, socleC2×C112×C13 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C3×C112
HallC2×C112×D13 ⋊ C3
HallC112×C13⋊C3 ⋊ C22
HallC112×C13 ⋊ C22×C3
HallC2×D13 ⋊ C3×C112
HallC13⋊C3 ⋊ C22×C112

Subgroups

subgroupG/H
center, hypercenterC2×C112D13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C112
FrattiniC1G
Fitting, socleC2×C112×C13C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C112

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3146

Conjugacy classes & character table

1936 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18876, 102);