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C22×C9×C53⋊C13 #37613593

order24804
automorphism?
homologyAbelianization (H1) = C22×C9×C13 · Schur multiplier (H2) = C2

Aliases

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

Splittings

Fitting, HallC22×C9×C53 ⋊ C13
derived, SylowC53 ⋊ C22×C9×C13
HallC9×C53 ⋊ C22×C13
HallC22×C53 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC22×C9C53⋊C13
commutator, hypocenterC53C22×C9×C13
FrattiniC3C22×C3×C53⋊C13
FittingC22×C9×C53C13
socleC22×C3×C53C3×C13
prime radicalC22×C3×C53⋊C13C3
cosocleC3×C53C22×C3×C13
LCSG ▷ C53
UCSC1 ◁ C22×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1908

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 25);