Finite Group Databasebeta

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C113×D13⋊C9 #40996229

order26442
automorphism?
homologyAbelianization (H1) = C2×C9×C113 · Schur multiplier (H2) = C1

Aliases

direct productC113×D13⋊C9
unambiguous semidirect productD13⋊(C9×C113)
unambiguous semidirect product(C13⋊C9)⋊(C2×C113)
unambiguous semidirect product(D13×C113)⋊C9

Splittings

derived, SylowC13 ⋊ C2×C9×C113
HallC113×C13⋊C9 ⋊ C2
HallD13×C113 ⋊ C9
HallC13×C113 ⋊ C2×C9
HallC13⋊C9 ⋊ C2×C113
HallD13 ⋊ C9×C113

Subgroups

subgroupG/H
center, hypercenterC3×C113D13⋊C3
commutator, hypocenterC13C2×C9×C113
FrattiniC3D13⋊C3×C113
Fitting, socleC3×C13×C113C2×C3
prime radicalC3×D13×C113C3
cosocleC3×C13C2×C3×C113
LCSG ▷ C13
UCSC1 ◁ C3×C113

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13221

Conjugacy classes & character table

2712 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26442, 11);