Finite Group Databasebeta

← Prev (#37561240) Next (#37561242) →

C2×C19⋊C3×C5⋊AGL(1,𝔽7) #37561241

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

Aliases

direct productC2×C19⋊C3×C5⋊AGL(1,𝔽7)
unambiguous semidirect product(C2×C5)⋊(AGL(1,𝔽7)×C19⋊C3)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(D5×C19⋊C3)
unambiguous semidirect product(C2×C19×C5⋊AGL(1,𝔽7))⋊C3
unambiguous semidirect product(C2×C5⋊#11716325)⋊C3
unambiguous semidirect product(C2×C5⋊#11716326)⋊C3
unambiguous semidirect product(C2×C19⋊C3×D35)⋊C3

Splittings

Fitting, socleC2×C5×C7×C19 ⋊ C2×C32
derived, HallC5×C7×C19 ⋊ C22×C32
HallC5×ΓL(1,𝔽8)×C19⋊C3 ⋊ C22
HallC2×C19×D35 ⋊ C32
HallΓL(1,𝔽8)×C19⋊C3 ⋊ C2×D5
HallC2×D35 ⋊ C3×C19⋊C3
HallC7×C19 ⋊ C2×C32×D5
HallC5×C19 ⋊ C2×C3×AGL(1,𝔽7)
HallC5×C7 ⋊ C22×C3×C19⋊C3
SylowC19 ⋊ C2×C3×C5⋊AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×D5×C19⋊C3
SylowC5 ⋊ C2×AGL(1,𝔽7)×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C19⋊C3×C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7×C19C22×C32
FrattiniC1G
Fitting, socleC2×C5×C7×C19C2×C32
LCSG ▷ C5×C7×C19
UCSC1 ◁ C2

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 1330

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 373);