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C5×C3⋊(C11⋊(D31⋊C3)) #44501854

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

Aliases

direct productC5×C3⋊(C11⋊(D31⋊C3))
unambiguous semidirect productC3⋊(C5×C11⋊(D31⋊C3))
unambiguous semidirect product(C5×D1023)⋊C3

Splittings

Fitting, socleC3×C5×C11×C31 ⋊ C2×C3
derivedC3×C11×C31 ⋊ C2×C3×C5
HallC3×C5×C11×C31⋊C3 ⋊ C2
HallC3×C11×C31⋊C3 ⋊ C2×C5
HallC5×C11×C31 ⋊ C3×D3
HallC3×C5×C31⋊C3 ⋊ D11
HallC11×C31 ⋊ C3×C5×D3
HallC3×C31⋊C3 ⋊ C5×D11
HallC5×C31 ⋊ C3×D33
HallC5×C11 ⋊ C3⋊(D31⋊C3)
SylowC31 ⋊ C3×C5×D33
SylowC11 ⋊ C5×C3⋊(D31⋊C3)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C11⋊(D31⋊C3))
commutator, cosocle, hypocenterC3×C11×C31C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C31C2×C3
LCSG ▷ C3×C11×C31
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5115

Conjugacy classes & character table

1095 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 221);