Finite Group Databasebeta

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C2×C3×C11×D55 #20300128

order7260
isoclinismisoclinic class of D55
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C11×D55
unambiguous semidirect product(C2×C5)⋊(C3×C11×D11)
unambiguous semidirect product(C2×C11)⋊(C3×D5×C11)

Splittings

Fitting, socleC2×C3×C5×C112 ⋊ C2
derivedC5×C11 ⋊ C22×C3×C11
HallC3×C5×C112 ⋊ C22
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, hypercenterC2×C3×C11D55
commutator, hypocenterC5×C11C22×C3×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C112C2
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1914 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C9×C11×D55, C2×C3×C5⋊#10624391, C3×D3×C11×D55, …
maximal normal subgroup ofC2×C9×C11×D55, C2×C32×C11×D55, C2×C3×C11×C5⋊AGL(1,𝔽11), …
maximal quotient ofC2×C9×C11×D55, C3×D3×C11×D55, C2×C32×C11×D55, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 228);