Finite Group Databasebeta

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C2×C3×C11⋊(D19⋊C3) #21419031

order7524
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C11⋊(D19⋊C3)
unambiguous semidirect product(C2×C11)⋊(C3×D19⋊C3)
unambiguous semidirect product(C2×C19⋊C3)⋊(C3×D11)
unambiguous semidirect product(C2×D209)⋊C32
unambiguous semidirect product(C2×C3×D209)⋊C3

Splittings

Fitting, socleC2×C3×C11×C19 ⋊ C2×C3
derived, HallC11×C19 ⋊ C22×C32
HallC3×C11×C19⋊C3 ⋊ C22
HallC2×D209 ⋊ C32
HallC3×C19⋊C3 ⋊ C2×D11
SylowC19 ⋊ C2×C32×D11
SylowC11 ⋊ C2×C3×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊(D19⋊C3)
commutator, hypocenterC11×C19C22×C32
FrattiniC1G
Fitting, socleC2×C3×C11×C19C2×C3
LCSG ▷ C11×C19
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

324 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×(C11⋊C5)⋊(D19⋊C3), C3×D5×C11⋊(D19⋊C3), C2×C3×C5×C11⋊(D19⋊C3), …
maximal normal subgroup ofC2×C3×(C11⋊C5)⋊(D19⋊C3), C2×C3×C5×C11⋊(D19⋊C3)
maximal quotient ofC3×D5×C11⋊(D19⋊C3), C2×C3×C5×C11⋊(D19⋊C3), C2×C3×C5⋊(C11⋊(D19⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7524, 75);