Finite Group Databasebeta

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C5×C11×C3⋊D57 #34037899

order18810
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC5×C11×C3⋊D57
unambiguous semidirect productC3⋊(C5×C11×D57)
unambiguous semidirect productC19⋊(C5×C11×C3⋊D3)

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C2
derived, HallC32×C19 ⋊ C2×C5×C11
HallC32×C11×C19 ⋊ C2×C5
HallC5×C11×C19 ⋊ C3⋊D3
HallC32×C5×C19 ⋊ C2×C11
HallC32×C5×C11 ⋊ D19
HallC11×C19 ⋊ C5×C3⋊D3
HallC32×C11 ⋊ C5×D19
HallC5×C19 ⋊ C11×C3⋊D3
HallC32×C5 ⋊ C11×D19
SylowC19 ⋊ C5×C11×C3⋊D3
SylowC32 ⋊ C5×C11×D19

Subgroups

subgroupG/H
center, hypercenterC5×C11C3⋊D57
commutator, cosocle, hypocenterC32×C19C2×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C19C2
LCSG ▷ C32×C19
UCSC1 ◁ C5×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

4785 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×C11×D57, C5×D33⋊D57, C11×D15⋊D57, …
maximal normal subgroup ofC5×D3×C11×D57, C5×D33⋊D57, C11×D15⋊D57, …
maximal quotient ofC5×C11×C3⋊Dic57, C2×C5×C11×C3⋊D57

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 92);