Finite Group Databasebeta

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C3×C3⋊(Dic89⋊C11) #47976497

order35244
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(Dic89⋊C11)
unambiguous semidirect productC3⋊(C3×Dic89⋊C11)
unambiguous semidirect productDic267⋊(C3×C11)
unambiguous semidirect product(C3×Dic267)⋊C11

Splittings

derivedC3×C89 ⋊ C3×C4×C11
HallC32×C89⋊C11 ⋊ C4
HallC3×Dic267 ⋊ C11
HallC89⋊C11 ⋊ C3×Dic3
HallC32×C89 ⋊ C4×C11
SylowC89 ⋊ C3×C11×Dic3
SylowC32 ⋊ Dic89⋊C11

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(D89⋊C11)
commutator, hypocenterC3×C89C3×C4×C11
FrattiniC2C3×C3⋊(D89⋊C11)
Fitting, socleC2×C32×C89C2×C11
prime radicalC2×C32×C89⋊C11C2
cosocleC2×C3×C89C2×C3×C11
LCSG ▷ C3×C89
UCSC1 ◁ C2×C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1068

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35244, 43);