Finite Group Databasebeta

← Prev (#28358473) Next (#28358475) →

C3×C5×D5×C31⋊C3 #28358474

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

Aliases

direct productC3×C5×D5×C31⋊C3
unambiguous semidirect productC5⋊(C2×C3×C5×C31⋊C3)
unambiguous semidirect product(C5×D5×C31)⋊C32
unambiguous semidirect product(C3×C5×D5×C31)⋊C3

Splittings

Fitting, socleC3×C52×C31 ⋊ C2×C3
derivedC5×C31 ⋊ C2×C32×C5
HallC3×C52×C31⋊C3 ⋊ C2
HallC5×D5×C31 ⋊ C32
HallC52×C31 ⋊ C2×C32
SylowC31 ⋊ C32×C5×D5
SylowC52 ⋊ C2×C3×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C5D5×C31⋊C3
commutator, cosocle, hypocenterC5×C31C2×C32×C5
FrattiniC1G
Fitting, socleC3×C52×C31C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

780 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×D5×D31⋊C3, C3×C5×(C31⋊C3)⋊AGL(1,𝔽5), C3×C5×AGL(1,𝔽5)×C31⋊C3, …
maximal normal subgroup ofC3×C5×D5×D31⋊C3, C3×C5×(C31⋊C3)⋊AGL(1,𝔽5), C3×C5×AGL(1,𝔽5)×C31⋊C3, …
maximal quotient ofC3×C5×Dic5×C31⋊C3, C2×C3×C5×D5×C31⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 117);