Finite Group Databasebeta

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C5×C7×C22⋊(C13⋊C9) #30655168

order16380
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C5×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC5×C7×C22⋊(C13⋊C9)
unambiguous semidirect productC22⋊(C5×C7×C13⋊C9)
unambiguous semidirect productC13⋊(C5×C7×C22⋊C9)
unambiguous semidirect product(C22×C5)⋊(C7×C13⋊C9)
unambiguous semidirect product(C5×C13)⋊(C7×C22⋊C9)

Splittings

derived, HallC22×C13 ⋊ C5×C7×C9
HallC22×C5×C7×C13 ⋊ C9
HallC5×C7×C13 ⋊ C22⋊C9
HallC22×C7×C13 ⋊ C5×C9
HallC22×C5×C13 ⋊ C7×C9
HallC22×C5×C7 ⋊ C13⋊C9
HallC7×C13 ⋊ C5×C22⋊C9
HallC5×C13 ⋊ C7×C22⋊C9
HallC22×C7 ⋊ C5×C13⋊C9
HallC22×C5 ⋊ C7×C13⋊C9
SylowC13 ⋊ C5×C7×C22⋊C9
SylowC22 ⋊ C5×C7×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C5×C7×C9
FrattiniC3C5×C7×C22⋊(C13⋊C3)
Fitting, socle, prime radicalC22×C3×C5×C7×C13C3
cosocleC22×C3×C13C3×C5×C7
LCSG ▷ C22×C13
UCSC1 ◁ C3×C5×C7

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8190

Conjugacy classes & character table

2100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 218);