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C9×AGL(1,𝔽5)×C131 #37556045

order23580
automorphism?
homologyAbelianization (H1) = C4×C9×C131 · Schur multiplier (H2) = C1

Aliases

direct productC9×AGL(1,𝔽5)×C131

Splittings

Fitting, HallC5×C9×C131 ⋊ C4
derived, SylowC5 ⋊ C4×C9×C131
HallC5×C131 ⋊ C4×C9
HallC5×C9 ⋊ C4×C131

Subgroups

subgroupG/H
center, hypercenterC9×C131AGL(1,𝔽5)
commutator, hypocenterC5C4×C9×C131
FrattiniC3C3×AGL(1,𝔽5)×C131
FittingC5×C9×C131C4
socleC3×C5×C131C3×C4
prime radicalC3×D5×C131C2×C3
cosocleC3×D5C2×C3×C131
LCSG ▷ C5
UCSC1 ◁ C9×C131

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5895

Conjugacy classes & character table

5895 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23580, 20);