Finite Group Databasebeta

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C2×C3⋊((C11⋊C5)⋊D11) #20300068

order7260
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊((C11⋊C5)⋊D11)
unambiguous semidirect product(C2×C3)⋊((C11⋊C5)⋊D11)
unambiguous semidirect product(C2×C11⋊C5)⋊D33

Splittings

Fitting, socleC2×C3×C112 ⋊ C2×C5
derived, HallC3×C112 ⋊ C22×C5
HallC3×C11×C11⋊C5 ⋊ C22
HallC2×C3⋊(C11⋊D11) ⋊ C5
HallC11×C11⋊C5 ⋊ C2×D3
SylowC112 ⋊ C2×C5×D3
SylowC3 ⋊ C2×(C11⋊C5)⋊D11

Subgroups

subgroupG/H
center, hypercenterC2C3⋊((C11⋊C5)⋊D11)
commutator, hypocenterC3×C112C22×C5
FrattiniC1G
Fitting, socleC2×C3×C112C2×C5
LCSG ▷ C3×C112
UCSC1 ◁ C2

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C9⋊((C11⋊C5)⋊D11), D3×C3⋊((C11⋊C5)⋊D11), C2×C3×C3⋊((C11⋊C5)⋊D11), …
maximal normal subgroup ofC2×C3×C3⋊((C11⋊C5)⋊D11), C2×C3⋊((C11⋊C5)⋊AGL(1,𝔽11)), C2×C5×C3⋊((C11⋊C5)⋊D11)
maximal quotient ofC2×C9⋊((C11⋊C5)⋊D11), D3×C3⋊((C11⋊C5)⋊D11), C2×C3×C3⋊((C11⋊C5)⋊D11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 168);