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C3⋊D3×C31×C11⋊C5 #44501833

order30690
automorphism?
homologyAbelianization (H1) = C2×C5×C31 · Schur multiplier (H2) = C3

Aliases

direct productC3⋊D3×C31×C11⋊C5
unambiguous semidirect productC3⋊(D3×C31×C11⋊C5)
unambiguous semidirect product(C11×C3⋊D3)⋊(C5×C31)

Splittings

Fitting, socle, HallC32×C11×C31 ⋊ C2×C5
derived, HallC32×C11 ⋊ C2×C5×C31
HallC32×C31×C11⋊C5 ⋊ C2
HallC11×C3⋊D3×C31 ⋊ C5
HallC32×C11⋊C5 ⋊ C2×C31
HallC11×C31 ⋊ C5×C3⋊D3
HallC32×C31 ⋊ C2×C11⋊C5
HallC11×C3⋊D3 ⋊ C5×C31
SylowC11 ⋊ C5×C3⋊D3×C31
SylowC32 ⋊ C2×C31×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC31C3⋊D3×C11⋊C5
commutator, cosocle, hypocenterC32×C11C2×C5×C31
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C32×C11
UCSC1 ◁ C31

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

1302 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 200);