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C11⋊C5×D31⋊C3 #23779481

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

Aliases

direct productC11⋊C5×D31⋊C3
unambiguous semidirect product(C11⋊C5×D31)⋊C3

Splittings

Fitting, socle, derived, HallC11×C31 ⋊ C2×C3×C5
HallC11⋊C5×C31⋊C3 ⋊ C2
HallC11⋊C5×D31 ⋊ C3
HallC11×D31⋊C3 ⋊ C5
HallC31×C11⋊C5 ⋊ C2×C3
HallC11×C31⋊C3 ⋊ C2×C5
HallC11×D31 ⋊ C3×C5
HallC31⋊C3 ⋊ C2×C11⋊C5
HallD31 ⋊ C3×C11⋊C5
SylowC31 ⋊ C2×C3×C11⋊C5
SylowC11 ⋊ C5×D31⋊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

77 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D31⋊C3, C2×C11⋊C5×D31⋊C3, C3×C11⋊C5×D31⋊C3, …
maximal normal subgroup ofAGL(1,𝔽11)×D31⋊C3, C2×C11⋊C5×D31⋊C3, C3×C11⋊C5×D31⋊C3
maximal quotient ofC11⋊C5×(C31⋊C3)⋊C4, C2×C11⋊C5×D31⋊C3, C11⋊C5×D31⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 80);