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C5×D11×#4296 #34037858

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

Aliases

direct productC5×D11×#4296

Splittings

Fitting, socle, HallC5×C11×C19 ⋊ C2×C9
derived, HallC11×C19 ⋊ C2×C5×C9
HallC5×C11×#4296 ⋊ C2
HallC5×C19×D11 ⋊ C9
HallC11×#4296 ⋊ C2×C5
HallC19×D11 ⋊ C5×C9
HallC5×C19 ⋊ C9×D11
HallC5×C11 ⋊ C2×#4296
SylowC19 ⋊ C5×C9×D11
SylowC11 ⋊ C2×C5×#4296

Subgroups

subgroupG/H
center, hypercenterC5D11×#4296
commutator, hypocenterC11×C19C2×C5×C9
FrattiniC1G
Fitting, socleC5×C11×C19C2×C9
prime radicalC5×D11×C19⋊C3C3
cosocleC11×C19⋊C3C2×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1045

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D11×AGL(1,𝔽19), D11×C5⋊AGL(1,𝔽19), D5×D11×#4296, …
maximal normal subgroup ofC5×D11×AGL(1,𝔽19), D11×C5⋊AGL(1,𝔽19), D5×D11×#4296, …
maximal quotient ofC5×Dic11×#4296, C2×C5×D11×#4296

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 51);