Finite Group Databasebeta

← Prev (#37561239) Next (#37561241) →

C2×C5⋊(ΓL(1,𝔽8)⋊(D19⋊C3)) #37561240

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

Aliases

direct productC2×C5⋊(ΓL(1,𝔽8)⋊(D19⋊C3))
unambiguous semidirect product(C2×C5)⋊(ΓL(1,𝔽8)⋊(D19⋊C3))
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C5⋊(D19⋊C3))
unambiguous semidirect product(C2×C19⋊C3)⋊(C5⋊AGL(1,𝔽7))
unambiguous semidirect product(C2×C5⋊#11716327)⋊C3
unambiguous semidirect product(C2×C5⋊#11716328)⋊C3
unambiguous semidirect product(C2×C5⋊(ΓL(1,𝔽8)⋊D19))⋊C3
unambiguous semidirect product(C2×C5⋊((C19⋊C3)⋊D7))⋊C3

Splittings

Fitting, socleC2×C5×C7×C19 ⋊ C2×C32
derived, HallC5×C7×C19 ⋊ C22×C32
HallC5×ΓL(1,𝔽8)×C19⋊C3 ⋊ C22
HallC2×D665 ⋊ C32
HallΓL(1,𝔽8)×C19⋊C3 ⋊ C2×D5
HallC7×C19 ⋊ C2×C32×D5
HallC5×C19 ⋊ C2×C3×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D19⋊C3
SylowC19 ⋊ C2×C3×C5⋊AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×C5⋊(D19⋊C3)
SylowC5 ⋊ C2×ΓL(1,𝔽8)⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(ΓL(1,𝔽8)⋊(D19⋊C3))
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 62 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 62 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

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 372);