Finite Group Databasebeta

← Prev (#22547697) Next (#22547699) →

C3×C7×C19×AGL(1,𝔽5) #22547698

order7980
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C19×AGL(1,𝔽5)

Splittings

Fitting, socle, HallC3×C5×C7×C19 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C7×C19
HallC5×C7×C19 ⋊ C3×C4
HallC3×C5×C19 ⋊ C4×C7
HallC3×C5×C7 ⋊ C4×C19
HallC5×C19 ⋊ C3×C4×C7
HallC5×C7 ⋊ C3×C4×C19
HallC3×C5 ⋊ C4×C7×C19

Subgroups

subgroupG/H
center, hypercenterC3×C7×C19AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C7×C19
FrattiniC1G
Fitting, socleC3×C5×C7×C19C4
LCSG ▷ C5
UCSC1 ◁ C3×C7×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1995 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×AGL(1,𝔽5)×#4294, C19×AGL(1,𝔽5)×C7⋊C9, AGL(1,𝔽5)×#11924776, …
maximal normal subgroup ofC7×AGL(1,𝔽5)×#4294, C19×AGL(1,𝔽5)×C7⋊C9, AGL(1,𝔽5)×#11924776, …
maximal quotient ofC7×C9×C19×AGL(1,𝔽5), C32×C7×C19×AGL(1,𝔽5), C3×C7×C19×ΓL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 123);