Finite Group Databasebeta

← Prev (#11764359) Next (#11764361) →

C3×C4×C31⋊C3 #11764360

order1116
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C31⋊C3
unambiguous semidirect product(C4×C31)⋊C32
unambiguous semidirect product(C3×C4×C31)⋊C3

Splittings

FittingC3×C4×C31 ⋊ C3
derived, SylowC31 ⋊ C32×C4
HallC4×C31 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C4C31⋊C3
commutator, hypocenterC31C32×C4
FrattiniC2C2×C3×C31⋊C3
FittingC3×C4×C31C3
socleC2×C3×C31C2×C3
prime radicalC2×C3×C31⋊C3C2
cosocleC2×C31C2×C32
LCSG ▷ C31
UCSC1 ◁ C3×C4

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 372

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×Dic11×C31⋊C3, C3×C4×C11×C31⋊C3, C31⋊C3×Dic13⋊C3, …
maximal normal subgroup ofC3×C4×C11×C31⋊C3, C3×C4×C13×C31⋊C3, C3×C4×C17×C31⋊C3, …
maximal quotient ofC3×Dic11×C31⋊C3, C3×C4×C11×C31⋊C3, C31⋊C3×Dic13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1116, 19);