Finite Group Databasebeta

← Prev (#40996238) Next (#40996240) →

C2×C3×C13⋊C3×C113 #40996239

order26442
automorphism?
homologyAbelianization (H1) = C2×C32×C113 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C13⋊C3×C113
unambiguous semidirect product(C2×C13)⋊(C32×C113)
unambiguous semidirect product(C2×C3×C13)⋊(C3×C113)
unambiguous semidirect product(C2×C13×C113)⋊C32
unambiguous semidirect product(C2×C3×C13×C113)⋊C3

Splittings

Fitting, socleC2×C3×C13×C113 ⋊ C3
derived, SylowC13 ⋊ C2×C32×C113
HallC2×C13×C113 ⋊ C32
HallC13×C113 ⋊ C2×C32
HallC2×C13 ⋊ C32×C113

Subgroups

subgroupG/H
center, hypercenterC2×C3×C113C13⋊C3
commutator, cosocle, hypocenterC13C2×C32×C113
FrattiniC1G
Fitting, socleC2×C3×C13×C113C3
LCSG ▷ C13
UCSC1 ◁ C2×C3×C113

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8814

Conjugacy classes & character table

4746 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26442, 21);