Finite Group Databasebeta

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D5×C11×D57 #27160076

order12540
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productD5×C11×D57
unambiguous semidirect product(C3×D5)⋊(C11×D19)
unambiguous semidirect product(D5×C19)⋊(D3×C11)

Splittings

Fitting, socle, HallC3×C5×C11×C19 ⋊ C22
derived, HallC3×C5×C19 ⋊ C22×C11
HallC5×C11×C19 ⋊ C2×D3
HallC3×C11×C19 ⋊ C2×D5
HallC11×C19 ⋊ D3×D5
HallC3×C5×C11 ⋊ C2×D19
HallC5×C19 ⋊ C2×D3×C11
HallC3×C19 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×D57
HallC3×C11 ⋊ D5×D19
SylowC19 ⋊ D3×D5×C11
HallC3×C5 ⋊ C2×C11×D19
SylowC5 ⋊ C2×C11×D57
SylowC3 ⋊ D5×C11×D19

Subgroups

subgroupG/H
center, hypercenterC11D5×D57
commutator, cosocle, hypocenterC3×C5×C19C22×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C19C22
LCSG ▷ C3×C5×C19
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD5×C11×D171, D5×C11×C3⋊(D19⋊C3), C3×D5×C11×D57, …
maximal normal subgroup ofD5×C11×C3⋊(D19⋊C3), C3×D5×C11×D57
maximal quotient ofD5×C11×D171, C3×D5×C11×D57, C11×D15×D57, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12540, 106);