Finite Group Databasebeta

← Prev (#28408207) Next (#28408209) →

C13×C3⋊((C31⋊C3)⋊C4) #28408208

order14508
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊((C31⋊C3)⋊C4)
unambiguous semidirect productC3⋊(C13×(C31⋊C3)⋊C4)
unambiguous semidirect product(C31⋊C3)⋊(Dic3×C13)
unambiguous semidirect productDic93⋊(C3×C13)

Splittings

derivedC3×C31 ⋊ C3×C4×C13
HallC3×C13×C31⋊C3 ⋊ C4
HallC13×C31 ⋊ C3×Dic3
HallC3×C31⋊C3 ⋊ C4×C13
SylowC31 ⋊ C3×Dic3×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊(D31⋊C3)
commutator, hypocenterC3×C31C3×C4×C13
FrattiniC2C13×C3⋊(D31⋊C3)
Fitting, socleC2×C3×C13×C31C2×C3
prime radicalC2×C3×C13×C31⋊C3C2
cosocleC2×C3×C31C2×C3×C13
LCSG ▷ C3×C31
UCSC1 ◁ C2×C13

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4836

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14508, 94);