Finite Group Databasebeta

← Prev (#37561273) Next (#37561275) →

C3×D5×C19×AGL(1,𝔽7) #37561274

order23940
automorphism?
homologyAbelianization (H1) = C22×C32×C19 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×D5×C19×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C32×D5×C19)
unambiguous semidirect product(D5×D7)⋊(C32×C19)
unambiguous semidirect product(C5×AGL(1,𝔽7))⋊(C2×C3×C19)
unambiguous semidirect product(D5×ΓL(1,𝔽8))⋊(C2×C3×C19)
unambiguous semidirect product(C5⋊AGL(1,𝔽7))⋊(C2×C3×C19)
unambiguous semidirect product(C3×D5×D7)⋊(C3×C19)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C22×C3
derived, HallC5×C7 ⋊ C22×C32×C19
HallC3×C5×C19×ΓL(1,𝔽8) ⋊ C22
HallD5×D7×C19 ⋊ C32
HallC3×C19×ΓL(1,𝔽8) ⋊ C2×D5
HallC5×C7×C19 ⋊ C22×C32
HallC3×C5×ΓL(1,𝔽8) ⋊ C22×C19
HallD5×D7 ⋊ C32×C19
HallC7×C19 ⋊ C2×C32×D5
HallC5×C19 ⋊ C2×C3×AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ C2×D5×C19
SylowC7 ⋊ C2×C32×D5×C19
SylowC5 ⋊ C2×C3×C19×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC3×C19D5×AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C22×C32×C19
FrattiniC1G
Fitting, socleC3×C5×C7×C19C22×C3
LCSG ▷ C5×C7
UCSC1 ◁ C3×C19

240 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1995

Conjugacy classes & character table

1596 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 406);