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C31⋊C3×AGL(1,𝔽11) #23779487

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

Aliases

direct productC31⋊C3×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C31⋊C3)
unambiguous semidirect product(C11⋊C5)⋊(C2×C31⋊C3)
unambiguous semidirect product(C31×AGL(1,𝔽11))⋊C3

Splittings

Fitting, socle, derived, HallC11×C31 ⋊ C2×C3×C5
HallC11⋊C5×C31⋊C3 ⋊ C2
HallC31×AGL(1,𝔽11) ⋊ C3
HallD11×C31⋊C3 ⋊ C5
HallC31×C11⋊C5 ⋊ C2×C3
HallC11×C31⋊C3 ⋊ C2×C5
HallD11×C31 ⋊ C3×C5
HallC11⋊C5 ⋊ C2×C31⋊C3
SylowC31 ⋊ C3×AGL(1,𝔽11)
HallD11 ⋊ C5×C31⋊C3
SylowC11 ⋊ C2×C5×C31⋊C3

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 →

Conjugacy classes & character table

143 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D31⋊C3, C2×C31⋊C3×AGL(1,𝔽11), C3×C31⋊C3×AGL(1,𝔽11), …
maximal normal subgroup ofAGL(1,𝔽11)×D31⋊C3, C2×C31⋊C3×AGL(1,𝔽11), C3×C31⋊C3×AGL(1,𝔽11)
maximal quotient ofC31⋊C3×Dic11⋊C5, C2×C31⋊C3×AGL(1,𝔽11), AGL(1,𝔽11)×C31⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 86);