Finite Group Databasebeta

← Prev (#26044521) Next (#26044523) →

C2×C19⋊(D31⋊C5) #26044522

order11780
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C19⋊(D31⋊C5)
unambiguous semidirect product(C2×C19)⋊(D31⋊C5)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊D19
unambiguous semidirect product(C2×D589)⋊C5

Splittings

Fitting, socleC2×C19×C31 ⋊ C2×C5
derived, HallC19×C31 ⋊ C22×C5
HallC19×ΓL(1,𝔽32) ⋊ C22
HallC2×D589 ⋊ C5
HallΓL(1,𝔽32) ⋊ C2×D19
SylowC31 ⋊ C2×C5×D19
SylowC19 ⋊ C2×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C19⋊(D31⋊C5)
commutator, cosocle, hypocenterC19×C31C22×C5
FrattiniC1G
Fitting, socleC2×C19×C31C2×C5
LCSG ▷ C19×C31
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#16812976⋊C5, C2×#16812975⋊C5, C2×(C19⋊C3)⋊(D31⋊C5), …
maximal normal subgroup ofC2×#16812976⋊C5, C2×#16812975⋊C5, C2×(C19⋊C3)⋊(D31⋊C5), …
maximal quotient ofD3×C19⋊(D31⋊C5), C2×C3×C19⋊(D31⋊C5), C2×C3⋊(C19⋊(D31⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11780, 16);