Finite Group Databasebeta

← Prev (#26010414) Next (#26010416) →

C22×#14583709 #26010415

order11008
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×#14583709

Splittings

FittingC22×AGL(1,ℤ/8)×C43 ⋊ C2
SylowC43 ⋊ C22×#577

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC22×AGL(1,ℤ/8)×C43C2
socleC23×C43C22×D4
hypercenterC22×AGL(1,ℤ/8)D43
hypocenterC43C22×#577
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

11118 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1083386);