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C9×C31⋊AGL(1,𝔽5) #19150047

order5580
automorphism?
homologyAbelianization (H1) = C4×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×C31⋊AGL(1,𝔽5)

Splittings

Fitting, HallC5×C9×C31 ⋊ C4
derived, HallC5×C31 ⋊ C4×C9
HallC9×C31 ⋊ AGL(1,𝔽5)
HallC5×C9 ⋊ Dic31
SylowC31 ⋊ C9×AGL(1,𝔽5)
SylowC5 ⋊ C9×Dic31

Subgroups

subgroupG/H
center, hypercenterC9C31⋊AGL(1,𝔽5)
commutator, hypocenterC5×C31C4×C9
FrattiniC3C3×C31⋊AGL(1,𝔽5)
FittingC5×C9×C31C4
socleC3×C5×C31C3×C4
LCSG ▷ C5×C31
UCSC1 ◁ C9

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

585 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×C31⋊#1035, C9×ΓL(1,𝔽32)⋊AGL(1,𝔽5), C5×C9×C31⋊AGL(1,𝔽5), …
maximal normal subgroup ofC9×ΓL(1,𝔽32)⋊AGL(1,𝔽5), C5×C9×C31⋊AGL(1,𝔽5)
maximal quotient ofC9×C31⋊#1035, C5×C9×C31⋊AGL(1,𝔽5), C9×C31⋊#1043, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 36);