Finite Group Databasebeta

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C11⋊C5×C3⋊D57 #34037874

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

Aliases

direct productC11⋊C5×C3⋊D57
unambiguous semidirect productC3⋊(C11⋊C5×D57)
unambiguous semidirect productC19⋊(C3⋊D3×C11⋊C5)
unambiguous semidirect product(C11×C3⋊D57)⋊C5

Splittings

Fitting, socle, derived, HallC32×C11×C19 ⋊ C2×C5
HallC32×C19×C11⋊C5 ⋊ C2
HallC11×C3⋊D57 ⋊ C5
HallC19×C11⋊C5 ⋊ C3⋊D3
HallC32×C11⋊C5 ⋊ D19
HallC11×C19 ⋊ C5×C3⋊D3
HallC32×C19 ⋊ C2×C11⋊C5
HallC32×C11 ⋊ C5×D19
SylowC19 ⋊ C3⋊D3×C11⋊C5
SylowC11 ⋊ C5×C3⋊D57
SylowC32 ⋊ D19×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C19C2×C5
LCSG ▷ C32×C11×C19
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1881

Conjugacy classes & character table

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

Relationships

maximal subgroup of(C3⋊AGL(1,𝔽11))⋊D57, D3×C11⋊C5×D57, AGL(1,𝔽11)×C3⋊D57, …
maximal normal subgroup of(C3⋊AGL(1,𝔽11))⋊D57, D3×C11⋊C5×D57, AGL(1,𝔽11)×C3⋊D57, …
maximal quotient ofC11⋊C5×C3⋊Dic57, C2×C11⋊C5×C3⋊D57

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 67);