Finite Group Databasebeta

← Prev (#20301594) Next (#20301596) →

D3×C3⋊(D41⋊C5) #20301595

order7380
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD3×C3⋊(D41⋊C5)
unambiguous semidirect product(C3×D3)⋊(D41⋊C5)
unambiguous semidirect product(D3×C41⋊C5)⋊D3
unambiguous semidirect product(D3×D123)⋊C5

Splittings

Fitting, socle, derived, HallC32×C41 ⋊ C22×C5
HallC32×C41⋊C5 ⋊ C22
HallD3×D123 ⋊ C5
HallC41⋊C5 ⋊ D32
SylowC41 ⋊ C5×D32
SylowC32 ⋊ C2×D41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C41C22×C5
LCSG ▷ C32×C41
UCSC1

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

81 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×C3⋊(D41⋊C5), D3×C3⋊(C5⋊(D41⋊C5)), D15×C3⋊(D41⋊C5), …
maximal normal subgroup ofC5×D3×C3⋊(D41⋊C5), D32×D41⋊C5
maximal quotient ofD3×C3⋊(D41⋊C25), C5×D3×C3⋊(D41⋊C5), D3×C3⋊(C5⋊(D41⋊C5)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 73);