Finite Group Databasebeta

← Prev (#28358460) Next (#28358462) →

C32×C5⋊(D31⋊C5) #28358461

order13950
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5⋊(D31⋊C5)
unambiguous semidirect productC5⋊(C32×D31⋊C5)
unambiguous semidirect product(C32×D155)⋊C5

Splittings

Fitting, socleC32×C5×C31 ⋊ C2×C5
derivedC5×C31 ⋊ C2×C32×C5
HallC32×C5×ΓL(1,𝔽32) ⋊ C2
HallC5×ΓL(1,𝔽32) ⋊ C2×C32
HallC32×C31 ⋊ C5×D5
SylowC31 ⋊ C32×C5×D5

Subgroups

subgroupG/H
center, hypercenterC32C5⋊(D31⋊C5)
commutator, cosocle, hypocenterC5×C31C2×C32×C5
FrattiniC1G
Fitting, socleC32×C5×C31C2×C5
LCSG ▷ C5×C31
UCSC1 ◁ C32

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

315 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×D5×D31⋊C5, C3×D3×C5⋊(D31⋊C5), C3×D15⋊(D31⋊C5), …
maximal normal subgroup ofC32×D5×D31⋊C5, C3×D3×C5⋊(D31⋊C5), C3×D15⋊(D31⋊C5), …
maximal quotient ofC32×ΓL(1,𝔽32)⋊Dic5, C2×C32×C5⋊(D31⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 104);