Finite Group Databasebeta

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C11×C3⋊D285 #34037895

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

Aliases

direct productC11×C3⋊D285
unambiguous semidirect productC3⋊(C11×D285)
unambiguous semidirect productC5⋊(C11×C3⋊D57)
unambiguous semidirect productC19⋊(C11×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C2
derived, HallC32×C5×C19 ⋊ C2×C11
HallC32×C11×C19 ⋊ D5
HallC5×C11×C19 ⋊ C3⋊D3
HallC32×C5×C11 ⋊ D19
HallC11×C19 ⋊ C3⋊D15
HallC32×C19 ⋊ D5×C11
HallC32×C11 ⋊ D95
HallC5×C19 ⋊ C11×C3⋊D3
HallC5×C11 ⋊ C3⋊D57
HallC32×C5 ⋊ C11×D19
SylowC19 ⋊ C11×C3⋊D15
SylowC32 ⋊ C11×D95
SylowC5 ⋊ C11×C3⋊D57

Subgroups

subgroupG/H
center, hypercenterC11C3⋊D285
commutator, cosocle, hypocenterC32×C5×C19C2×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C19C2
LCSG ▷ C32×C5×C19
UCSC1 ◁ C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

4719 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C11×D285, C11×D15×D57, D33⋊D285, …
maximal normal subgroup ofD3×C11×D285, C11×D15×D57, D33⋊D285, …
maximal quotient ofC11×C3⋊Dic285, C2×C11×C3⋊D285

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 88);