Finite Group Databasebeta

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C11×C5⋊(#4294⋊C2) #34037838

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

Aliases

direct productC11×C5⋊(#4294⋊C2)
unambiguous semidirect productC5⋊(C11×#4294⋊C2)
unambiguous semidirect product#4294⋊(D5×C11)

Splittings

derived, HallC5×C19 ⋊ C2×C9×C11
HallC5×C11×#4294 ⋊ C2
HallC11×D95 ⋊ C9
HallC11×#4294 ⋊ D5
HallC5×C11×C19 ⋊ C2×C9
HallC5×#4294 ⋊ C2×C11
HallC11×C19 ⋊ C9×D5
HallD95 ⋊ C9×C11
Hall#4294 ⋊ D5×C11
HallC5×C11 ⋊ #4294⋊C2
SylowC19 ⋊ C9×D5×C11
SylowC5 ⋊ C11×#4294⋊C2

Subgroups

subgroupG/H
center, hypercenterC3×C11C5⋊(D19⋊C3)
commutator, hypocenterC5×C19C2×C9×C11
FrattiniC3C11×C5⋊(D19⋊C3)
Fitting, socleC3×C5×C11×C19C2×C3
prime radicalC3×C11×D95C3
cosocleC3×C5×C19C2×C3×C11
LCSG ▷ C5×C19
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD5×C11×#4294⋊C2, D11×C5⋊(#4294⋊C2), D55⋊(#4294⋊C2), …
maximal normal subgroup ofD5×C11×#4294⋊C2, D11×C5⋊(#4294⋊C2), D55⋊(#4294⋊C2), …
maximal quotient ofC11×#4294⋊Dic5, C2×C11×C5⋊(#4294⋊C2)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 31);