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C5×D3×C43⋊C7 #22583293

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

Aliases

direct productC5×D3×C43⋊C7
unambiguous semidirect productC3⋊(C2×C5×C43⋊C7)
unambiguous semidirect product(D3×C43)⋊(C5×C7)
unambiguous semidirect product(C5×D3×C43)⋊C7

Splittings

Fitting, socle, HallC3×C5×C43 ⋊ C2×C7
derived, HallC3×C43 ⋊ C2×C5×C7
HallC3×C5×C43⋊C7 ⋊ C2
HallC5×D3×C43 ⋊ C7
HallC3×C43⋊C7 ⋊ C2×C5
HallD3×C43 ⋊ C5×C7
HallC5×C43 ⋊ D3×C7
SylowC43 ⋊ C5×D3×C7
HallC3×C5 ⋊ C2×C43⋊C7
SylowC3 ⋊ C2×C5×C43⋊C7

Subgroups

subgroupG/H
center, hypercenterC5D3×C43⋊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

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×D43⋊C7, D3×C5⋊(D43⋊C7), D3×D5×C43⋊C7, …
maximal normal subgroup ofC5×D3×D43⋊C7, D3×C5⋊(D43⋊C7), D3×D5×C43⋊C7, …
maximal quotient ofC5×Dic3×C43⋊C7, C2×C5×D3×C43⋊C7, C5×D9×C43⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9030, 26);