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C5×C3⋊(D43⋊C7) #22583294

order9030
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(D43⋊C7)
unambiguous semidirect productC3⋊(C5×D43⋊C7)
unambiguous semidirect productD129⋊(C5×C7)
unambiguous semidirect product(C43⋊C7)⋊(C5×D3)
unambiguous semidirect product(C5×D129)⋊C7

Splittings

Fitting, socle, HallC3×C5×C43 ⋊ C2×C7
derived, HallC3×C43 ⋊ C2×C5×C7
HallC3×C5×C43⋊C7 ⋊ C2
HallC5×C43⋊C7 ⋊ D3
HallC5×D129 ⋊ C7
HallC3×C43⋊C7 ⋊ C2×C5
HallC43⋊C7 ⋊ C5×D3
HallD129 ⋊ C5×C7
HallC5×C43 ⋊ D3×C7
SylowC43 ⋊ C5×D3×C7
HallC3×C5 ⋊ D43⋊C7
SylowC3 ⋊ C5×D43⋊C7

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(D43⋊C7)
commutator, hypocenterC3×C43C2×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C43C2×C7
LCSG ▷ C3×C43
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×D43⋊C7, D5×C3⋊(D43⋊C7), D15⋊(D43⋊C7), …
maximal normal subgroup ofC5×D3×D43⋊C7, D5×C3⋊(D43⋊C7), D15⋊(D43⋊C7), …
maximal quotient ofC5×C3⋊(Dic43⋊C7), C2×C5×C3⋊(D43⋊C7), C5×C9⋊(D43⋊C7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9030, 27);