Finite Group Databasebeta

← Prev (#20258306) Next (#20258308) →

C3×C5⋊(D67⋊C3) #20258307

order6030
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5⋊(D67⋊C3)
unambiguous semidirect productC5⋊(C3×D67⋊C3)
unambiguous semidirect product(C67⋊C3)⋊(C3×D5)
unambiguous semidirect productD335⋊C32
unambiguous semidirect product(C3×D335)⋊C3

Splittings

Fitting, socleC3×C5×C67 ⋊ C2×C3
derived, HallC5×C67 ⋊ C2×C32
HallC3×C5×C67⋊C3 ⋊ C2
HallD335 ⋊ C32
HallC3×C67⋊C3 ⋊ D5
SylowC67 ⋊ C32×D5
SylowC5 ⋊ C3×D67⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C5⋊(D67⋊C3)
commutator, hypocenterC5×C67C2×C32
FrattiniC1G
Fitting, socleC3×C5×C67C2×C3
LCSG ▷ C5×C67
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

201 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×D67⋊C3, D3×C5⋊(D67⋊C3), D15⋊(D67⋊C3), …
maximal normal subgroup ofC3×D5×D67⋊C3, D3×C5⋊(D67⋊C3), D15⋊(D67⋊C3), …
maximal quotient ofC3×(C67⋊C3)⋊Dic5, C2×C3×C5⋊(D67⋊C3), C3×C25⋊(D67⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6030, 15);