Finite Group Databasebeta

← Prev (#36370317) Next (#36370319) →

AGL(1,ℤ/8)×#10621924 #36370318

order22144
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#10621924

Splittings

FittingAGL(1,ℤ/8)×C173 ⋊ C4
SylowC173 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#10621924
commutatorC4×C173C23×C4
FrattiniC4C23×#10621924
FittingAGL(1,ℤ/8)×C173C4
socleC2×C173C2×C4×D4
prime radicalAGL(1,ℤ/8)×D173C2
cosocleC4×D173C24
hypercenterAGL(1,ℤ/8)#10621924
hypocenterC173C4×AGL(1,ℤ/8)
LCSG ▷ C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1384

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 21265);