Finite Group Databasebeta

← Prev (#11745540) Next (#11745542) →

C2×C3×C4×C13⋊C3 #11745541

order936
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C4×C13⋊C3
unambiguous semidirect product(C2×C4×C13)⋊C32
unambiguous semidirect product(C2×C3×C4×C13)⋊C3

Splittings

FittingC2×C3×C4×C13 ⋊ C3
derived, SylowC13 ⋊ C2×C32×C4
HallC2×C4×C13 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4C13⋊C3
commutator, hypocenterC13C2×C32×C4
FrattiniC2C22×C3×C13⋊C3
FittingC2×C3×C4×C13C3
socleC22×C3×C13C2×C3
prime radicalC22×C3×C13⋊C3C2
cosocleC2×C13C22×C32
LCSG ▷ C13
UCSC1 ◁ C2×C3×C4

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 312

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×#1055⋊C3, C3×#6099⋊C3, C3×C4×Dic13⋊C3, …
maximal normal subgroup ofC2×C3×#1055⋊C3, C3×#6099⋊C3, C3×C4×Dic13⋊C3, …
maximal quotient ofC3×C42×C13⋊C3, C3×C22⋊C4×C13⋊C3, C3×C4⋊C4×C13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(936, 134);