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C3×(C31⋊C3)⋊AGL(1,𝔽5) #19150113

order5580
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C31⋊C3)⋊AGL(1,𝔽5)
unambiguous semidirect product(C31⋊C3)⋊(C3×AGL(1,𝔽5))
unambiguous semidirect product(C31⋊AGL(1,𝔽5))⋊C32
unambiguous semidirect product(C3×C31⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, socleC3×C5×C31 ⋊ C3×C4
derived, HallC5×C31 ⋊ C32×C4
HallC3×C5×C31⋊C3 ⋊ C4
HallC31⋊AGL(1,𝔽5) ⋊ C32
HallC3×C31⋊C3 ⋊ AGL(1,𝔽5)
SylowC31 ⋊ C32×AGL(1,𝔽5)
SylowC5 ⋊ C3×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC3(C31⋊C3)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C31C32×C4
FrattiniC1G
Fitting, socleC3×C5×C31C3×C4
LCSG ▷ C5×C31
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(C31⋊C3)⋊#1035, C3×((C31⋊C3)⋊C5)⋊AGL(1,𝔽5), C3×C5×(C31⋊C3)⋊AGL(1,𝔽5), …
maximal normal subgroup ofC3×((C31⋊C3)⋊C5)⋊AGL(1,𝔽5), C3×C5×(C31⋊C3)⋊AGL(1,𝔽5)
maximal quotient ofC3×(C31⋊C3)⋊#1035, C3×C5×(C31⋊C3)⋊AGL(1,𝔽5), C3×(C31⋊C3)⋊#1042, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 102);