Finite Group Databasebeta

← Prev (#23779476) Next (#23779478) →

C11×C5⋊(D31⋊C3) #23779477

order10230
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C5⋊(D31⋊C3)
unambiguous semidirect productC5⋊(C11×D31⋊C3)
unambiguous semidirect product(C31⋊C3)⋊(D5×C11)
unambiguous semidirect productD155⋊(C3×C11)
unambiguous semidirect product(C11×D155)⋊C3

Splittings

Fitting, socle, HallC5×C11×C31 ⋊ C2×C3
derived, HallC5×C31 ⋊ C2×C3×C11
HallC5×C11×C31⋊C3 ⋊ C2
HallC11×D155 ⋊ C3
HallC11×C31⋊C3 ⋊ D5
HallC5×C31⋊C3 ⋊ C2×C11
HallC11×C31 ⋊ C3×D5
HallD155 ⋊ C3×C11
HallC31⋊C3 ⋊ D5×C11
HallC5×C11 ⋊ D31⋊C3
SylowC31 ⋊ C3×D5×C11
SylowC5 ⋊ C11×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC11C5⋊(D31⋊C3)
commutator, cosocle, hypocenterC5×C31C2×C3×C11
FrattiniC1G
Fitting, socleC5×C11×C31C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C11×D31⋊C3, D11×C5⋊(D31⋊C3), D55⋊(D31⋊C3), …
maximal normal subgroup ofD5×C11×D31⋊C3, D11×C5⋊(D31⋊C3), D55⋊(D31⋊C3), …
maximal quotient ofC11×(C31⋊C3)⋊Dic5, C2×C11×C5⋊(D31⋊C3), C11×C5⋊(D31⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 76);