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C3×C5×C3⋊(D31⋊C5) #28358463

order13950
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5×C3⋊(D31⋊C5)
unambiguous semidirect productC3⋊(C3×C5×D31⋊C5)
unambiguous semidirect product(C3×D93)⋊C52
unambiguous semidirect product(C3×C5×D93)⋊C5

Splittings

Fitting, socleC32×C5×C31 ⋊ C2×C5
derivedC3×C31 ⋊ C2×C3×C52
HallC32×C5×ΓL(1,𝔽32) ⋊ C2
HallC5×ΓL(1,𝔽32) ⋊ C3×D3
HallC3×D93 ⋊ C52
HallC32×C31 ⋊ C2×C52
SylowC31 ⋊ C3×C52×D3
SylowC32 ⋊ C5×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊(D31⋊C5)
commutator, cosocle, hypocenterC3×C31C2×C3×C52
FrattiniC1G
Fitting, socleC32×C5×C31C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C3×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

360 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×D3×D31⋊C5, C3×D5×C3⋊(D31⋊C5), C3×D15⋊(D31⋊C5), …
maximal normal subgroup ofC3×C5×D3×D31⋊C5, C3×D5×C3⋊(D31⋊C5), C3×D15⋊(D31⋊C5), …
maximal quotient ofC3×C5×C3⋊(Dic31⋊C5), C2×C3×C5×C3⋊(D31⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 106);