Finite Group Databasebeta

← Prev (#13088263) Next (#13088265) →

C23×C9×AGL(1,𝔽5) #13088264

order1440
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C23×C4×C9 · Schur multiplier (H2) = C26

Aliases

direct productC23×C9×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C22×C4×C9)

Splittings

FittingC23×C5×C9 ⋊ C4
derived, SylowC5 ⋊ C23×C4×C9
HallC5×C9 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC23×C9AGL(1,𝔽5)
commutator, hypocenterC5C23×C4×C9
FrattiniC3C23×C3×AGL(1,𝔽5)
FittingC23×C5×C9C4
socleC23×C3×C5C3×C4
prime radicalC23×C3×D5C2×C3
cosocleC3×D5C24×C3
LCSG ▷ C5
UCSC1 ◁ C23×C9

708 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 360

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4581);