Finite Group Databasebeta

← Prev (#28358482) Next (#28358484) →

C3×D31⋊(C52⋊C3) #28358483

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

Aliases

direct productC3×D31⋊(C52⋊C3)
unambiguous semidirect product(C3×D31)⋊(C52⋊C3)

Splittings

Fitting, socleC3×C52×C31 ⋊ C2×C3
derived, HallC52×C31 ⋊ C2×C32
HallC3×C52⋊(C31⋊C3) ⋊ C2
HallC52×D31 ⋊ C32
HallD31 ⋊ C3×C52⋊C3
SylowC31 ⋊ C2×C3×C52⋊C3
SylowC52 ⋊ C3×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC3D31⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C31C2×C32
FrattiniC1G
Fitting, socleC3×C52×C31C2×C3
LCSG ▷ C52×C31
UCSC1 ◁ C3

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

441 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D31⋊((C5⋊D5)⋊C3), D3×D31⋊(C52⋊C3), D31⋊(C3⋊((C5⋊D5)⋊C3)), …
maximal normal subgroup ofC3×D31⋊((C5⋊D5)⋊C3), D3×D31⋊(C52⋊C3), D31⋊(C3⋊((C5⋊D5)⋊C3)), …
maximal quotient ofC3×Dic31⋊(C52⋊C3), C2×C3×D31⋊(C52⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 126);