Finite Group Databasebeta

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C53×C22⋊(C13⋊C9) #37613623

order24804
automorphism?
homologyAbelianization (H1) = C9×C53 · Schur multiplier (H2) = C2

Aliases

direct productC53×C22⋊(C13⋊C9)
unambiguous semidirect productC22⋊(C53×C13⋊C9)
unambiguous semidirect productC13⋊(C22⋊C9×C53)
unambiguous semidirect product(C22×C53)⋊(C13⋊C9)
unambiguous semidirect product(C13×C53)⋊(C22⋊C9)

Splittings

derived, HallC22×C13 ⋊ C9×C53
HallC22×C13×C53 ⋊ C9
HallC13×C53 ⋊ C22⋊C9
HallC22×C53 ⋊ C13⋊C9
SylowC13 ⋊ C22⋊C9×C53
SylowC22 ⋊ C53×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C53C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C9×C53
FrattiniC3C53×C22⋊(C13⋊C3)
Fitting, socle, prime radicalC22×C3×C13×C53C3
cosocleC22×C3×C13C3×C53
LCSG ▷ C22×C13
UCSC1 ◁ C3×C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12402

Conjugacy classes & character table

3180 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 55);