Finite Group Databasebeta

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C3×D5×C11×D11 #20300089

order7260
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×C11×D11
unambiguous semidirect product(D5×C11)⋊(C2×C3×C11)
unambiguous semidirect product(C5×D11)⋊(C2×C3×C11)
unambiguous semidirect productD55⋊(C2×C3×C11)

Splittings

Fitting, socle, HallC3×C5×C112 ⋊ C22
derivedC5×C11 ⋊ C22×C3×C11
HallC5×C112 ⋊ C22×C3
HallC3×C112 ⋊ C2×D5
SylowC112 ⋊ C2×C3×D5
HallC3×C5 ⋊ C2×C11×D11
SylowC5 ⋊ C2×C3×C11×D11

Subgroups

subgroupG/H
center, hypercenterC3×C11D5×D11
commutator, hypocenterC5×C11C22×C3×C11
FrattiniC1G
Fitting, socleC3×C5×C112C22
LCSG ▷ C5×C11
UCSC1 ◁ C3×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

924 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×D5×C11×D11, C3×D5×#10624391, C32×D5×C11×D11, …
maximal normal subgroup ofC9×D5×C11×D11, C32×D5×C11×D11, C3×D5×C11×AGL(1,𝔽11), …
maximal quotient ofC9×D5×C11×D11, C32×D5×C11×D11, C3×C11×D11×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 189);