Finite Group Databasebeta

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C5×D11×#4294 #34037835

order18810
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×D11×#4294

Splittings

derived, HallC11×C19 ⋊ C2×C5×C9
HallC5×C11×#4294 ⋊ C2
HallC5×C19×D11 ⋊ C9
HallC11×#4294 ⋊ C2×C5
HallC5×C11×C19 ⋊ C2×C9
HallC19×D11 ⋊ C5×C9
HallC5×C19 ⋊ C9×D11
HallC5×C11 ⋊ C2×#4294
SylowC19 ⋊ C5×C9×D11
SylowC11 ⋊ C2×C5×#4294

Subgroups

subgroupG/H
center, hypercenterC3×C5D11×C19⋊C3
commutator, hypocenterC11×C19C2×C5×C9
FrattiniC3C5×D11×C19⋊C3
Fitting, socleC3×C5×C11×C19C2×C3
prime radicalC3×C5×C19×D11C3
cosocleC3×C11×C19C2×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D11×#4294⋊C2, D11×C5⋊(#4294⋊C2), D5×D11×#4294, …
maximal normal subgroup ofC5×D11×#4294⋊C2, D11×C5⋊(#4294⋊C2), D5×D11×#4294, …
maximal quotient ofC5×Dic11×#4294, C2×C5×D11×#4294

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 28);