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C3×#16811772⋊C2 #35205705

order20460
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×#16811772⋊C2

Splittings

Fitting, socle, HallC3×C11×C31 ⋊ C22×C5
derived, HallC11×C31 ⋊ C22×C3×C5
HallC3×#13133723 ⋊ C22
HallC3×D11×D31 ⋊ C5
Hall#13133723 ⋊ C22×C3
HallD11×D31 ⋊ C3×C5
HallC3×C31 ⋊ C2×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×D31⋊C5
SylowC31 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C3×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC3#16811772⋊C2
commutator, cosocle, hypocenterC11×C31C22×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C31C22×C5
LCSG ▷ C11×C31
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1023

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 125);