Finite Group Databasebeta

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C2×C5×C11×D57 #27160100

order12540
isoclinismisoclinic class of D57
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C11×D57
unambiguous semidirect product(C2×C3)⋊(C5×C11×D19)
unambiguous semidirect product(C2×C19)⋊(C5×D3×C11)

Splittings

Fitting, socleC2×C3×C5×C11×C19 ⋊ C2
derived, HallC3×C19 ⋊ C22×C5×C11
HallC3×C5×C11×C19 ⋊ C22
HallC5×C11×C19 ⋊ C2×D3
HallC3×C11×C19 ⋊ C22×C5
HallC3×C5×C19 ⋊ C22×C11
HallC11×C19 ⋊ C2×C5×D3
HallC3×C5×C11 ⋊ C2×D19
HallC5×C19 ⋊ C2×D3×C11
HallC3×C11 ⋊ C2×C5×D19
SylowC19 ⋊ C2×C5×D3×C11
HallC3×C5 ⋊ C2×C11×D19
SylowC3 ⋊ C2×C5×C11×D19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D57
commutator, cosocle, hypocenterC3×C19C22×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C19C2
LCSG ▷ C3×C19
UCSC1 ◁ C2×C5×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C11×D171, C2×C5×C11×C3⋊(D19⋊C3), C5×D3×C11×D57, …
maximal normal subgroup ofC2×C5×C11×C3⋊(D19⋊C3), C2×C3×C5×C11×D57
maximal quotient ofC2×C5×C11×D171, C5×D3×C11×D57, C2×C3×C5×C11×D57, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12540, 130);