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C5×D3×(C31⋊C3)⋊C5 #28358451

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

Aliases

direct productC5×D3×(C31⋊C3)⋊C5
unambiguous semidirect productC3⋊(C2×C5×(C31⋊C3)⋊C5)
unambiguous semidirect product(D3×C31⋊C3)⋊C52
unambiguous semidirect product(D3×ΓL(1,𝔽32))⋊(C3×C5)
unambiguous semidirect product(C5×D3×C31⋊C3)⋊C5
unambiguous semidirect product(C5×D3×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socleC3×C5×C31 ⋊ C2×C3×C5
derivedC3×C31 ⋊ C2×C3×C52
HallC3×C5×(C31⋊C3)⋊C5 ⋊ C2
HallC5×ΓL(1,𝔽32) ⋊ C3×D3
HallD3×C31⋊C3 ⋊ C52
HallC3×C31⋊C3 ⋊ C2×C52
SylowC31 ⋊ C3×C52×D3

Subgroups

subgroupG/H
center, hypercenterC5D3×(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC3×C31C2×C3×C52
FrattiniC1G
Fitting, socleC3×C5×C31C2×C3×C5
LCSG ▷ C3×C31
UCSC1 ◁ C5

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×AGL(1,𝔽31), D3×C5⋊AGL(1,𝔽31), D3×D5×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC5×D3×AGL(1,𝔽31), D3×C5⋊AGL(1,𝔽31), D3×D5×(C31⋊C3)⋊C5, …
maximal quotient ofC5×Dic3×(C31⋊C3)⋊C5, C2×C5×D3×(C31⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 94);