Finite Group Databasebeta

C7×C13×AGL(1,𝔽19) #44527639

order31122
automorphism?
homologyAbelianization (H1) = C2×C7×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×AGL(1,𝔽19)
unambiguous semidirect product#4296⋊(C2×C7×C13)

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C9
derived, SylowC19 ⋊ C2×C7×C9×C13
HallC7×C13×#4296 ⋊ C2
HallC7×C13×D19 ⋊ C9
HallC13×#4296 ⋊ C2×C7
HallC7×#4296 ⋊ C2×C13
HallC13×D19 ⋊ C7×C9
HallC7×D19 ⋊ C9×C13
HallC13×C19 ⋊ C2×C7×C9
Hall#4296 ⋊ C2×C7×C13
HallC7×C19 ⋊ C2×C9×C13
HallD19 ⋊ C7×C9×C13

Subgroups

subgroupG/H
center, hypercenterC7×C13AGL(1,𝔽19)
commutator, hypocenterC19C2×C7×C9×C13
FrattiniC1G
Fitting, socleC7×C13×C19C2×C9
prime radicalC7×C13×D19⋊C3C3
cosocleC19⋊C3C2×C3×C7×C13
LCSG ▷ C19
UCSC1 ◁ C7×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1729

Conjugacy classes & character table

1729 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 122);