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((C31⋊C3)⋊C5)⋊D11 #23779492

order10230
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product((C31⋊C3)⋊C5)⋊D11
unambiguous semidirect product(ΓL(1,𝔽32)⋊D11)⋊C3

Splittings

Fitting, socle, derived, HallC11×C31 ⋊ C2×C3×C5
HallC11×(C31⋊C3)⋊C5 ⋊ C2
HallΓL(1,𝔽32)⋊D11 ⋊ C3
HallC11⋊(D31⋊C3) ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C2×C3
HallC11×C31⋊C3 ⋊ C2×C5
HallD341 ⋊ C3×C5
Hall(C31⋊C3)⋊C5 ⋊ D11
HallΓL(1,𝔽32) ⋊ C3×D11
HallC31⋊C3 ⋊ C5×D11
SylowC31 ⋊ C3×C5×D11
SylowC11 ⋊ AGL(1,𝔽31)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,5,11,31|d^a=d^10,e^a=e^30,e^b=e^25,e^c=e^16

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×AGL(1,𝔽31), C2×((C31⋊C3)⋊C5)⋊D11, C3×((C31⋊C3)⋊C5)⋊D11, …
maximal normal subgroup ofD11×AGL(1,𝔽31), C2×((C31⋊C3)⋊C5)⋊D11, C3×((C31⋊C3)⋊C5)⋊D11
maximal quotient of((C31⋊C3)⋊C5)⋊Dic11, C2×((C31⋊C3)⋊C5)⋊D11, (ΓL(1,𝔽32)⋊C9)⋊D11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 91);