Finite Group Databasebeta

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C5×C11×#4294⋊C2 #34037834

order18810
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×#4294⋊C2
unambiguous semidirect product#4294⋊(C2×C5×C11)

Splittings

derived, SylowC19 ⋊ C2×C5×C9×C11
HallC5×C11×#4294 ⋊ C2
HallC5×C11×D19 ⋊ C9
HallC11×#4294 ⋊ C2×C5
HallC5×C11×C19 ⋊ C2×C9
HallC5×#4294 ⋊ C2×C11
HallC11×D19 ⋊ C5×C9
HallC11×C19 ⋊ C2×C5×C9
HallC5×D19 ⋊ C9×C11
Hall#4294 ⋊ C2×C5×C11
HallC5×C19 ⋊ C2×C9×C11
HallD19 ⋊ C5×C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11D19⋊C3
commutator, hypocenterC19C2×C5×C9×C11
FrattiniC3C5×C11×D19⋊C3
Fitting, socleC3×C5×C11×C19C2×C3
prime radicalC3×C5×C11×D19C3
cosocleC3×C19C2×C3×C5×C11
LCSG ▷ C19
UCSC1 ◁ C3×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D11×#4294⋊C2, D5×C11×#4294⋊C2, D55×#4294⋊C2, …
maximal normal subgroup ofC5×D11×#4294⋊C2, D5×C11×#4294⋊C2, D55×#4294⋊C2, …
maximal quotient ofC5×C11×#4294⋊C4, C2×C5×C11×#4294⋊C2

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 27);