Finite Group Databasebeta

← Prev (#34038319) Next (#34038321) →

C121×Dic13⋊C3 #34038320

order18876
automorphism?
homologyAbelianization (H1) = C3×C4×C121 · Schur multiplier (H2) = C1

Aliases

direct productC121×Dic13⋊C3
unambiguous semidirect productDic13⋊(C3×C121)
unambiguous semidirect product(Dic13×C121)⋊C3

Splittings

derived, SylowC13 ⋊ C3×C4×C121
HallDic13×C121 ⋊ C3
HallC13⋊C3×C121 ⋊ C4
HallC13×C121 ⋊ C3×C4
HallDic13 ⋊ C3×C121
HallC13⋊C3 ⋊ C4×C121

Subgroups

subgroupG/H
center, hypercenterC2×C121D13⋊C3
commutator, hypocenterC13C3×C4×C121
FrattiniC2×C11C11×D13⋊C3
FittingC2×C13×C121C2×C3
socle, cosocleC2×C11×C13C2×C3×C11
prime radicalC2×C11×C13⋊C3C2×C11
LCSG ▷ C13
UCSC1 ◁ C2×C121

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6292

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, 2);