Finite Group Databasebeta

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C5×C11⋊(#4294⋊C2) #34037836

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

Aliases

direct productC5×C11⋊(#4294⋊C2)
unambiguous semidirect product#4294⋊(C5×D11)

Splittings

derived, HallC11×C19 ⋊ C2×C5×C9
HallC5×C11×#4294 ⋊ C2
HallC5×D209 ⋊ C9
HallC11×#4294 ⋊ C2×C5
HallC5×C11×C19 ⋊ C2×C9
HallC5×#4294 ⋊ D11
HallD209 ⋊ C5×C9
Hall#4294 ⋊ C5×D11
HallC5×C19 ⋊ C9×D11
HallC5×C11 ⋊ #4294⋊C2
SylowC19 ⋊ C5×C9×D11
SylowC11 ⋊ C5×#4294⋊C2

Subgroups

subgroupG/H
center, hypercenterC3×C5C11⋊(D19⋊C3)
commutator, hypocenterC11×C19C2×C5×C9
FrattiniC3C5×C11⋊(D19⋊C3)
Fitting, socleC3×C5×C11×C19C2×C3
prime radicalC3×C5×D209C3
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

810 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, 29);