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C2×C5×(C11⋊C5)⋊D11 #27130941

order12100
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

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

Splittings

Fitting, socleC2×C5×C112 ⋊ C2×C5
derived, SylowC112 ⋊ C22×C52
HallC5×C11×C11⋊C5 ⋊ C22
HallC2×C11⋊D11 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC2×C5(C11⋊C5)⋊D11
commutator, cosocle, hypocenterC112C22×C52
FrattiniC1G
Fitting, socleC2×C5×C112C2×C5
LCSG ▷ C112
UCSC1 ◁ C2×C5

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

460 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×(C11⋊C5)⋊D11, C2×C3×C5×(C11⋊C5)⋊D11, C2×C5×C3⋊((C11⋊C5)⋊D11)
maximal normal subgroup ofC2×C3×C5×(C11⋊C5)⋊D11
maximal quotient ofC5×D3×(C11⋊C5)⋊D11, C2×C3×C5×(C11⋊C5)⋊D11, C2×C5×C3⋊((C11⋊C5)⋊D11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 220);