Finite Group Databasebeta

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C2×D13⋊C3×C121 #34038335

order18876
automorphism?
homologyAbelianization (H1) = C22×C3×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×D13⋊C3×C121
unambiguous semidirect productD13⋊(C2×C3×C121)
unambiguous semidirect product(C13⋊C3)⋊(C22×C121)
unambiguous semidirect product(C2×D13)⋊(C3×C121)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C121)
unambiguous semidirect product(C2×D13×C121)⋊C3

Splittings

FittingC2×C13×C121 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C3×C121
HallC2×D13×C121 ⋊ C3
HallC13⋊C3×C121 ⋊ C22
HallC13×C121 ⋊ C22×C3
HallC2×D13 ⋊ C3×C121
HallC13⋊C3 ⋊ C22×C121

Subgroups

subgroupG/H
center, hypercenterC2×C121D13⋊C3
commutator, hypocenterC13C22×C3×C121
FrattiniC11C2×C11×D13⋊C3
FittingC2×C13×C121C2×C3
socleC2×C11×C13C2×C3×C11
prime radicalC2×C11×D13⋊C3C11
cosocleC11×C13C22×C3×C11
LCSG ▷ C13
UCSC1 ◁ C2×C121

60 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, 17);