Finite Group Databasebeta

← Prev (#44501874) Next (#44501876) →

C3×C5×C11×D93 #44501875

order30690
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×D93
unambiguous semidirect productC3⋊(C3×C5×C11×D31)

Splittings

Fitting, socle, HallC32×C5×C11×C31 ⋊ C2
derivedC3×C31 ⋊ C2×C3×C5×C11
HallC32×C11×C31 ⋊ C2×C5
HallC5×C11×C31 ⋊ C3×D3
HallC32×C5×C31 ⋊ C2×C11
HallC32×C5×C11 ⋊ D31
HallC11×C31 ⋊ C3×C5×D3
HallC32×C31 ⋊ C2×C5×C11
HallC5×C31 ⋊ C3×D3×C11
HallC32×C11 ⋊ C5×D31
HallC32×C5 ⋊ C11×D31
SylowC31 ⋊ C3×C5×D3×C11
SylowC32 ⋊ C5×C11×D31

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11D93
commutator, cosocle, hypocenterC3×C31C2×C3×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C3×C31
UCSC1 ◁ C3×C5×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10230

Conjugacy classes & character table

7920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 242);