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C2×C3⋊(D181⋊C3) #20266804

order6516
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(D181⋊C3)
unambiguous semidirect product(C2×C3)⋊(D181⋊C3)
unambiguous semidirect product(C2×C181⋊C3)⋊D3
unambiguous semidirect product(C2×D543)⋊C3

Splittings

Fitting, socleC2×C3×C181 ⋊ C2×C3
derivedC3×C181 ⋊ C22×C3
HallC3×C181⋊C3 ⋊ C22
SylowC181 ⋊ C2×C3×D3

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(D181⋊C3)
commutator, hypocenterC3×C181C22×C3
FrattiniC1G
Fitting, socleC2×C3×C181C2×C3
LCSG ▷ C3×C181
UCSC1 ◁ C2

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3⋊((D181⋊C3)⋊C5), D5×C3⋊(D181⋊C3), C2×C5×C3⋊(D181⋊C3), …
maximal normal subgroup ofC2×C3⋊((D181⋊C3)⋊C5), C2×C5×C3⋊(D181⋊C3)
maximal quotient ofD5×C3⋊(D181⋊C3), C2×C5×C3⋊(D181⋊C3), C2×C3⋊(C5⋊(D181⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6516, 41);