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C3×C4×(C31⋊C3)⋊C5 #19150071

order5580
isoclinismisoclinic class of (C31⋊C3)⋊C5
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×(C31⋊C3)⋊C5
unambiguous semidirect product(C4×C31⋊C3)⋊(C3×C5)
unambiguous semidirect product(C4×ΓL(1,𝔽32))⋊C32
unambiguous semidirect product(C3×C4×C31⋊C3)⋊C5
unambiguous semidirect product(C3×C4×ΓL(1,𝔽32))⋊C3

Splittings

FittingC3×C4×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C32×C4×C5
HallC3×C4×C31⋊C3 ⋊ C5
HallC4×ΓL(1,𝔽32) ⋊ C32
HallC3×C31⋊C3 ⋊ C4×C5
HallΓL(1,𝔽32) ⋊ C32×C4
HallC4×C31 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4(C31⋊C3)⋊C5
commutator, hypocenterC31C32×C4×C5
FrattiniC2C2×C3×(C31⋊C3)⋊C5
FittingC3×C4×C31C3×C5
socleC2×C3×C31C2×C3×C5
LCSG ▷ C31
UCSC1 ◁ C3×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×Dic5×(C31⋊C3)⋊C5, C3×C4×C5×(C31⋊C3)⋊C5, C3×AGL(1,𝔽5)×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC3×C4×C5×(C31⋊C3)⋊C5, C3×C4×AGL(1,𝔽31), C4×D3×(C31⋊C3)⋊C5, …
maximal quotient ofC3×C4×(C31⋊C3)⋊C25, C3×Dic5×(C31⋊C3)⋊C5, C3×C4×C5×(C31⋊C3)⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 60);