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C22×(C43⋊C7)⋊C9 #24925442

order10836
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC22×(C43⋊C7)⋊C9
unambiguous semidirect product(C22×C43⋊C9)⋊C7

Splittings

derived, SylowC43 ⋊ C22×C7×C9
HallC22×C43⋊C9 ⋊ C7
HallC22×C43⋊C7 ⋊ C9
HallC43⋊C9 ⋊ C22×C7
HallC43⋊C7 ⋊ C22×C9
HallC22×C43 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC22×C3(C43⋊C3)⋊C7
commutator, hypocenterC43C22×C7×C9
FrattiniC3C22×(C43⋊C3)⋊C7
Fitting, socleC22×C3×C43C3×C7
prime radicalC22×C3×C43⋊C7C3
cosocleC3×C43C22×C3×C7
LCSG ▷ C43
UCSC1 ◁ C22×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

276 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 34);