Finite Group Databasebeta

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C3×C4×C89⋊C11 #26044317

order11748
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×C89⋊C11
unambiguous semidirect product(C4×C89)⋊(C3×C11)
unambiguous semidirect product(C3×C4×C89)⋊C11

Splittings

Fitting, HallC3×C4×C89 ⋊ C11
derived, SylowC89 ⋊ C3×C4×C11
HallC4×C89 ⋊ C3×C11
HallC3×C89 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC3×C4C89⋊C11
commutator, hypocenterC89C3×C4×C11
FrattiniC2C2×C3×C89⋊C11
FittingC3×C4×C89C11
socleC2×C3×C89C2×C11
prime radicalC2×C3×C89⋊C11C2
cosocleC2×C89C2×C3×C11
LCSG ▷ C89
UCSC1 ◁ C3×C4

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C9×C89⋊C11, C3×Dic3×C89⋊C11, C32×C4×C89⋊C11
maximal normal subgroup ofC4×C9×C89⋊C11, C32×C4×C89⋊C11
maximal quotient ofC4×C9×C89⋊C11, C3×Dic3×C89⋊C11, C32×C4×C89⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11748, 2);