Finite Group Databasebeta

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C5×D11×C31⋊C3 #23779474

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

Aliases

direct productC5×D11×C31⋊C3
unambiguous semidirect product(C5×D11×C31)⋊C3

Splittings

Fitting, socle, HallC5×C11×C31 ⋊ C2×C3
derived, HallC11×C31 ⋊ C2×C3×C5
HallC5×C11×C31⋊C3 ⋊ C2
HallC5×D11×C31 ⋊ C3
HallC11×C31⋊C3 ⋊ C2×C5
HallD11×C31 ⋊ C3×C5
HallC5×C31 ⋊ C3×D11
HallC5×C11 ⋊ C2×C31⋊C3
SylowC31 ⋊ C3×C5×D11
SylowC11 ⋊ C2×C5×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D11×C31⋊C3
commutator, cosocle, hypocenterC11×C31C2×C3×C5
FrattiniC1G
Fitting, socleC5×C11×C31C2×C3
LCSG ▷ C11×C31
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

455 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D11×D31⋊C3, D11×C5⋊(D31⋊C3), D5×D11×C31⋊C3, …
maximal normal subgroup ofC5×D11×D31⋊C3, D11×C5⋊(D31⋊C3), D5×D11×C31⋊C3, …
maximal quotient ofC5×Dic11×C31⋊C3, C2×C5×D11×C31⋊C3, C5×D11×C31⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 73);