Finite Group Databasebeta

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C113×D63 #28382833

order14238
isoclinismisoclinic class of D63
automorphism?
homologyAbelianization (H1) = C2×C113 · Schur multiplier (H2) = C1

Aliases

direct productC113×D63
unambiguous semidirect productC7⋊(D9×C113)
unambiguous semidirect productC9⋊(D7×C113)

Splittings

Fitting, HallC7×C9×C113 ⋊ C2
derived, HallC7×C9 ⋊ C2×C113
HallC9×C113 ⋊ D7
HallC7×C113 ⋊ D9
SylowC9 ⋊ D7×C113
SylowC7 ⋊ D9×C113

Subgroups

subgroupG/H
center, hypercenterC113D63
commutator, cosocle, hypocenterC7×C9C2×C113
FrattiniC3D21×C113
FittingC7×C9×C113C2
socleC3×C7×C113D3
LCSG ▷ C7×C9
UCSC1 ◁ C113

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7119

Conjugacy classes & character table

3729 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD63×D113, D7×D9×C113, D63⋊D113, …
maximal normal subgroup ofD63×D113, D7×D9×C113, D63⋊D113, …
maximal quotient ofC113×Dic63, C2×C113×D63

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14238, 9);