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C11×((C31⋊C3)⋊C4)⋊C5 #35205659

order20460
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×((C31⋊C3)⋊C4)⋊C5
unambiguous semidirect product((C31⋊C3)⋊C4)⋊(C5×C11)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C4×C11)
unambiguous semidirect product(Dic31⋊C5)⋊(C3×C11)
unambiguous semidirect product(C11×Dic31⋊C5)⋊C3

Splittings

derived, SylowC31 ⋊ C3×C4×C5×C11
HallC11×Dic31⋊C5 ⋊ C3
HallC11×(C31⋊C3)⋊C5 ⋊ C4
HallC11×(C31⋊C3)⋊C4 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C3×C4
HallC11×Dic31 ⋊ C3×C5
HallC11×C31⋊C3 ⋊ C4×C5
HallDic31⋊C5 ⋊ C3×C11
Hall(C31⋊C3)⋊C5 ⋊ C4×C11
Hall(C31⋊C3)⋊C4 ⋊ C5×C11
HallC11×C31 ⋊ C3×C4×C5
HallΓL(1,𝔽32) ⋊ C3×C4×C11
HallDic31 ⋊ C3×C5×C11
HallC31⋊C3 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11AGL(1,𝔽31)
commutator, hypocenterC31C3×C4×C5×C11
FrattiniC2C11×AGL(1,𝔽31)
Fitting, socleC2×C11×C31C2×C3×C5
prime radicalC2×C11×(C31⋊C3)⋊C5C2
cosocleC2×C31C2×C3×C5×C11
LCSG ▷ C31
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1364

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 79);