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C11×D15⋊D11 #20300111

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

Aliases

direct productC11×D15⋊D11
unambiguous semidirect productD15⋊(C11×D11)
unambiguous semidirect productD33⋊(D5×C11)
unambiguous semidirect productD55⋊(D3×C11)

Splittings

Fitting, socle, HallC3×C5×C112 ⋊ C22
derivedC3×C5×C11 ⋊ C22×C11
HallC5×C112 ⋊ C2×D3
HallC3×C112 ⋊ C2×D5
SylowC112 ⋊ D3×D5
HallC3×C5 ⋊ C2×C11×D11
SylowC5 ⋊ D3×C11×D11
SylowC3 ⋊ D5×C11×D11

Subgroups

subgroupG/H
center, hypercenterC11D15⋊D11
commutator, hypocenterC3×C5×C11C22×C11
FrattiniC1G
Fitting, socleC3×C5×C112C22
LCSG ▷ C3×C5×C11
UCSC1 ◁ C11

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

627 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×D45⋊D11, D15⋊#10624391, C3×C11×D15⋊D11, …
maximal normal subgroup ofC3×C11×D15⋊D11, C11×D15⋊AGL(1,𝔽11), C11⋊C5×D15⋊D11, …
maximal quotient ofC11×D45⋊D11, C3×C11×D15⋊D11, C11×D33⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 211);