Finite Group Databasebeta

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C3×C11×D465 #44501879

order30690
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D465
unambiguous semidirect productC3⋊(C3×C11×D155)
unambiguous semidirect productC5⋊(C3×C11×D93)

Splittings

Fitting, socle, HallC32×C5×C11×C31 ⋊ C2
derivedC3×C5×C31 ⋊ C2×C3×C11
HallC32×C11×C31 ⋊ D5
HallC5×C11×C31 ⋊ C3×D3
HallC32×C5×C31 ⋊ C2×C11
HallC32×C5×C11 ⋊ D31
HallC11×C31 ⋊ C3×D15
HallC32×C31 ⋊ D5×C11
HallC5×C31 ⋊ C3×D3×C11
HallC32×C11 ⋊ D155
HallC5×C11 ⋊ C3×D93
HallC32×C5 ⋊ C11×D31
SylowC31 ⋊ C3×C11×D15
SylowC32 ⋊ C11×D155
SylowC5 ⋊ C3×C11×D93

Subgroups

subgroupG/H
center, hypercenterC3×C11D465
commutator, cosocle, hypocenterC3×C5×C31C2×C3×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C3×C5×C31
UCSC1 ◁ C3×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10230

Conjugacy classes & character table

7722 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 246);