Finite Group Databasebeta

← Prev (#37561221) Next (#37561223) →

C2×C5×C7×AGL(1,𝔽19) #37561222

order23940
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×AGL(1,𝔽19)
unambiguous semidirect product#4296⋊(C22×C5×C7)
unambiguous semidirect product(C2×#4296)⋊(C2×C5×C7)

Splittings

Fitting, socleC2×C5×C7×C19 ⋊ C2×C9
derived, SylowC19 ⋊ C22×C5×C7×C9
HallC5×C7×#4296 ⋊ C22
HallC2×C5×C7×D19 ⋊ C9
HallC7×#4296 ⋊ C22×C5
HallC5×#4296 ⋊ C22×C7
HallC5×C7×C19 ⋊ C22×C9
HallC2×C7×D19 ⋊ C5×C9
HallC2×C5×D19 ⋊ C7×C9
Hall#4296 ⋊ C22×C5×C7
HallC7×C19 ⋊ C22×C5×C9
HallC5×C19 ⋊ C22×C7×C9
HallC2×D19 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7AGL(1,𝔽19)
commutator, hypocenterC19C22×C5×C7×C9
FrattiniC1G
Fitting, socleC2×C5×C7×C19C2×C9
prime radicalC2×C5×C7×D19⋊C3C3
cosocleC19⋊C3C22×C3×C5×C7
LCSG ▷ C19
UCSC1 ◁ C2×C5×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1330

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 354);