Finite Group Databasebeta

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C3×C11×C307⋊C3 #44477247

order30393
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×C307⋊C3
unambiguous semidirect productC307⋊(C32×C11)
unambiguous semidirect product(C3×C307)⋊(C3×C11)
unambiguous semidirect product(C11×C307)⋊C32
unambiguous semidirect product(C3×C11×C307)⋊C3

Splittings

Fitting, socleC3×C11×C307 ⋊ C3
derived, SylowC307 ⋊ C32×C11
HallC11×C307 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C11C307⋊C3
commutator, cosocle, hypocenterC307C32×C11
FrattiniC1G
Fitting, socleC3×C11×C307C3
LCSG ▷ C307
UCSC1 ◁ C3×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10131

Conjugacy classes & character table

3465 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30393, 5);