Finite Group Databasebeta

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C2×C11⋊C5×#4296 #34037848

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

Aliases

direct productC2×C11⋊C5×#4296
unambiguous semidirect product(C2×C11)⋊(C5×#4296)
unambiguous semidirect product(C2×C11×#4296)⋊C5

Splittings

Fitting, socle, HallC2×C11×C19 ⋊ C5×C9
derived, HallC11×C19 ⋊ C2×C5×C9
HallC2×C11×#4296 ⋊ C5
HallC2×C19×C11⋊C5 ⋊ C9
HallC11×#4296 ⋊ C2×C5
HallC19×C11⋊C5 ⋊ C2×C9
HallC2×C19 ⋊ C9×C11⋊C5
HallC2×C11 ⋊ C5×#4296
SylowC19 ⋊ C2×C9×C11⋊C5
SylowC11 ⋊ C2×C5×#4296

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×#4296
commutator, hypocenterC11×C19C2×C5×C9
FrattiniC1G
Fitting, socleC2×C11×C19C5×C9
prime radicalC2×C11⋊C5×C19⋊C3C3
cosocleC11×C19⋊C3C2×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 418

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C11⋊C5)⋊(#4296⋊C4), #4296×Dic11⋊C5, C11⋊C5×#4296⋊C4, …
maximal normal subgroup of(C11⋊C5)⋊(#4296⋊C4), #4296×Dic11⋊C5, C11⋊C5×#4296⋊C4, …
maximal quotient ofC4×C11⋊C5×#4296, C22×C11⋊C5×#4296

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 41);