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C2×(C11⋊C5)⋊(D31⋊C3) #35205693

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

Aliases

direct productC2×(C11⋊C5)⋊(D31⋊C3)
unambiguous semidirect product(C2×C11⋊C5)⋊(D31⋊C3)
unambiguous semidirect product(C2×(C11⋊C5)⋊D31)⋊C3

Splittings

Fitting, socleC2×C11×C31 ⋊ C2×C3×C5
derived, HallC11×C31 ⋊ C22×C3×C5
HallC2×(C11⋊C5)⋊D31 ⋊ C3
HallC11⋊C5×C31⋊C3 ⋊ C22
HallC2×C11⋊(D31⋊C3) ⋊ C5
HallC31×C11⋊C5 ⋊ C22×C3
HallC2×D341 ⋊ C3×C5
HallC11×C31⋊C3 ⋊ C22×C5
HallC31⋊C3 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D31⋊C3
SylowC31 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2(C11⋊C5)⋊(D31⋊C3)
commutator, cosocle, hypocenterC11×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 682

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 113);