Finite Group Databasebeta

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C2×C5⋊((C11⋊D11)⋊C3) #20300077

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

Aliases

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

Splittings

Fitting, socleC2×C5×C112 ⋊ C2×C3
derived, HallC5×C112 ⋊ C22×C3
HallC2×C5⋊(C11⋊D11) ⋊ C3
HallC5×C112⋊C3 ⋊ C22
HallC112⋊C3 ⋊ C2×D5
SylowC112 ⋊ C2×C3×D5
SylowC5 ⋊ C2×(C11⋊D11)⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C5⋊((C11⋊D11)⋊C3)
commutator, hypocenterC5×C112C22×C3
FrattiniC1G
Fitting, socleC2×C5×C112C2×C3
LCSG ▷ C5×C112
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C5⋊((C11⋊D11)⋊C3), C2×C3×C5⋊((C11⋊D11)⋊C3), C2×C3⋊(C5⋊((C11⋊D11)⋊C3)), …
maximal normal subgroup ofC2×C3×C5⋊((C11⋊D11)⋊C3), C2×C5⋊(((C11⋊D11)⋊C3)⋊C5), C2×C5×C5⋊((C11⋊D11)⋊C3)
maximal quotient ofC2×C5⋊((C11⋊D11)⋊C9), D3×C5⋊((C11⋊D11)⋊C3), C2×C3×C5⋊((C11⋊D11)⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 177);