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C17×C22⋊(C43⋊C3) #22578568

order8772
automorphism?
homologyAbelianization (H1) = C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×C22⋊(C43⋊C3)
unambiguous semidirect productC22⋊(C17×C43⋊C3)
unambiguous semidirect productC43⋊(A4×C17)
unambiguous semidirect product(C22×C17)⋊(C43⋊C3)
unambiguous semidirect product(C17×C43)⋊A4

Splittings

Fitting, socle, HallC22×C17×C43 ⋊ C3
derived, HallC22×C43 ⋊ C3×C17
HallC17×C43 ⋊ A4
HallC22×C17 ⋊ C43⋊C3
SylowC43 ⋊ A4×C17
SylowC22 ⋊ C17×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC17C22⋊(C43⋊C3)
commutator, hypocenterC22×C43C3×C17
FrattiniC1G
Fitting, socleC22×C17×C43C3
LCSG ▷ C22×C43
UCSC1 ◁ C17

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1020 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4×C17×C43⋊C3, C3×C17×C22⋊(C43⋊C3)
maximal normal subgroup ofA4×C17×C43⋊C3, C3×C17×C22⋊(C43⋊C3)
maximal quotient ofC17×C22⋊(C43⋊C9), C3×C17×C22⋊(C43⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8772, 31);