Finite Group Databasebeta

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C52×C22⋊(C13⋊C9) #26043469

order11700
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C52×C9 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×C22⋊(C13⋊C9)
unambiguous semidirect productC22⋊(C52×C13⋊C9)
unambiguous semidirect productC13⋊(C52×C22⋊C9)
unambiguous semidirect product(C22×C5)⋊(C5×C13⋊C9)
unambiguous semidirect product(C5×C13)⋊(C5×C22⋊C9)

Splittings

derived, HallC22×C13 ⋊ C52×C9
HallC22×C52×C13 ⋊ C9
HallC52×C13 ⋊ C22⋊C9
HallC22×C52 ⋊ C13⋊C9
SylowC13 ⋊ C52×C22⋊C9
SylowC22 ⋊ C52×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C52C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C52×C9
FrattiniC3C52×C22⋊(C13⋊C3)
Fitting, socle, prime radicalC22×C3×C52×C13C3
cosocleC22×C3×C13C3×C52
LCSG ▷ C22×C13
UCSC1 ◁ C3×C52

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 316);