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C2×#16811774⋊C3 #35205696

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

Aliases

direct productC2×#16811774⋊C3
unambiguous semidirect product(C2×#16811774)⋊C3

Splittings

Fitting, socleC2×C11×C31 ⋊ C2×C3×C5
derived, HallC11×C31 ⋊ C22×C3×C5
HallC2×#16811774 ⋊ C3
Hall#13133724⋊C3 ⋊ C22
HallC2×C11×D31⋊C3 ⋊ C5
Hall#13133724 ⋊ C22×C3
HallC2×C11×D31 ⋊ C3×C5
HallC11×C31⋊C3 ⋊ C22×C5
HallC2×D31⋊C3 ⋊ C11⋊C5
HallC2×D31 ⋊ C3×C11⋊C5
HallC31⋊C3 ⋊ C22×C11⋊C5
SylowC31 ⋊ C22×C3×C11⋊C5
SylowC11 ⋊ C2×AGL(1,𝔽31)

Subgroups

subgroupG/H
center, hypercenterC2#16811774⋊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

106 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 116);