Finite Group Databasebeta

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C2×C3⋊(C5⋊(C11⋊D11)) #20300121

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

Aliases

direct productC2×C3⋊(C5⋊(C11⋊D11))
unambiguous semidirect product(C2×C3)⋊(C5⋊(C11⋊D11))
unambiguous semidirect product(C2×C5)⋊(C3⋊(C11⋊D11))
unambiguous semidirect product(C2×C11)⋊D165

Splittings

Fitting, socleC2×C3×C5×C112 ⋊ C2
derived, HallC3×C5×C112 ⋊ C22
HallC5×C112 ⋊ C2×D3
HallC3×C112 ⋊ C2×D5
SylowC112 ⋊ C2×D15
HallC3×C5 ⋊ C2×C11⋊D11
SylowC5 ⋊ C2×C3⋊(C11⋊D11)
SylowC3 ⋊ C2×C5⋊(C11⋊D11)

Subgroups

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

280 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1818 conjugacy classes. The character table is too large to display.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 221);