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C3×D5×(C31⋊C3)⋊C5 #28358449

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

Aliases

direct productC3×D5×(C31⋊C3)⋊C5
unambiguous semidirect productC5⋊(C2×C3×(C31⋊C3)⋊C5)
unambiguous semidirect product(D5×C31⋊C3)⋊(C3×C5)
unambiguous semidirect product(D5×ΓL(1,𝔽32))⋊C32
unambiguous semidirect product(C3×D5×C31⋊C3)⋊C5
unambiguous semidirect product(C3×D5×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socleC3×C5×C31 ⋊ C2×C3×C5
derivedC5×C31 ⋊ C2×C32×C5
HallC3×C5×(C31⋊C3)⋊C5 ⋊ C2
HallD5×ΓL(1,𝔽32) ⋊ C32
HallC5×ΓL(1,𝔽32) ⋊ C2×C32
HallC3×C31⋊C3 ⋊ C5×D5
SylowC31 ⋊ C32×C5×D5

Subgroups

subgroupG/H
center, hypercenterC3D5×(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC5×C31C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C31C2×C3×C5
LCSG ▷ C5×C31
UCSC1 ◁ C3

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×((C31⋊C3)⋊C5)⋊AGL(1,𝔽5), C3×AGL(1,𝔽5)×(C31⋊C3)⋊C5, C3×D5×AGL(1,𝔽31), …
maximal normal subgroup ofC3×((C31⋊C3)⋊C5)⋊AGL(1,𝔽5), C3×AGL(1,𝔽5)×(C31⋊C3)⋊C5, C3×D5×AGL(1,𝔽31), …
maximal quotient ofC3×Dic5×(C31⋊C3)⋊C5, C2×C3×D5×(C31⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 92);