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C5×C3⋊(D67⋊C3) #20258309

order6030
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(D67⋊C3)
unambiguous semidirect productC3⋊(C5×D67⋊C3)
unambiguous semidirect product(C67⋊C3)⋊(C5×D3)
unambiguous semidirect productD201⋊(C3×C5)
unambiguous semidirect product(C5×D201)⋊C3

Splittings

Fitting, socleC3×C5×C67 ⋊ C2×C3
derivedC3×C67 ⋊ C2×C3×C5
HallC3×C5×C67⋊C3 ⋊ C2
HallC3×C67⋊C3 ⋊ C2×C5
HallC5×C67 ⋊ C3×D3
SylowC67 ⋊ C3×C5×D3

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(D67⋊C3)
commutator, hypocenterC3×C67C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C67C2×C3
LCSG ▷ C3×C67
UCSC1 ◁ C5

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×D67⋊C3, D5×C3⋊(D67⋊C3), D15⋊(D67⋊C3), …
maximal normal subgroup ofC5×D3×D67⋊C3, D5×C3⋊(D67⋊C3), D15⋊(D67⋊C3), …
maximal quotient ofC5×C3⋊((C67⋊C3)⋊C4), C2×C5×C3⋊(D67⋊C3), C25×C3⋊(D67⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6030, 17);