Finite Group Databasebeta

← Prev (#36523843) Next (#36523845) →

AGL(1,ℤ/8)×#10623494 #36523844

order22784
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#10623494

Splittings

SylowC89 ⋊ C8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D4×D89
commutatorC4×C89C23×C8
FrattiniC42C23×D89
FittingC4×AGL(1,ℤ/8)×C89C2
socleC22×C89C2×C4×D4
prime radicalC2×AGL(1,ℤ/8)×C89C4
cosocleC42×C89C24
hypercenterC4×AGL(1,ℤ/8)D89
hypocenterC89C8×AGL(1,ℤ/8)
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

2024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 138984);