Finite Group Databasebeta

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C3×C11⋊C5×#595 #26014352

order11220
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊C5×#595
unambiguous semidirect product(C11×#595)⋊(C3×C5)
unambiguous semidirect product(C3×C11×#595)⋊C5

Splittings

Fitting, socle, HallC3×C11×C17 ⋊ C4×C5
derived, HallC11×C17 ⋊ C3×C4×C5
HallC3×C17×C11⋊C5 ⋊ C4
HallC3×C11×#595 ⋊ C5
HallC17×C11⋊C5 ⋊ C3×C4
HallC11×#595 ⋊ C3×C5
HallC3×C17 ⋊ C4×C11⋊C5
HallC3×C11 ⋊ C5×#595
SylowC17 ⋊ C3×C4×C11⋊C5
SylowC11 ⋊ C3×C5×#595

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×#595
commutator, hypocenterC11×C17C3×C4×C5
FrattiniC1G
Fitting, socleC3×C11×C17C4×C5
prime radicalC3×D17×C11⋊C5C2
cosocleC11×D17C2×C3×C5
LCSG ▷ C11×C17
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×C11⋊C5×#595, C32×C11⋊C5×#595, C3×C11⋊C5×C3⋊#595
maximal normal subgroup ofC9×C11⋊C5×#595, C32×C11⋊C5×#595
maximal quotient ofC9×C11⋊C5×#595, C32×C11⋊C5×#595, C3×C11⋊C5×C3⋊#595

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 28);