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C9×AGL(1,𝔽5)×C31 #19150046

order5580
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C9×C31 · Schur multiplier (H2) = C1

Aliases

direct productC9×AGL(1,𝔽5)×C31

Splittings

Fitting, HallC5×C9×C31 ⋊ C4
derived, SylowC5 ⋊ C4×C9×C31
HallC5×C31 ⋊ C4×C9
HallC5×C9 ⋊ C4×C31

Subgroups

subgroupG/H
center, hypercenterC9×C31AGL(1,𝔽5)
commutator, hypocenterC5C4×C9×C31
FrattiniC3C3×AGL(1,𝔽5)×C31
FittingC5×C9×C31C4
socleC3×C5×C31C3×C4
LCSG ▷ C5
UCSC1 ◁ C9×C31

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1395 conjugacy classes. The character table is too large to display.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 35);