Finite Group Databasebeta

C2×#26021541 #36582292

order22784
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#26021541

Splittings

SylowC89 ⋊ C2×#2051

Subgroups

subgroupG/H
centerC23#15667984
commutator, cosocleC22×C4×C89C24
FrattiniC22×C4C23×D89
Fitting, prime radicalC22×AGL(1,ℤ/8)×C89C2
socleC23×C89#121
hypercenterC22×AGL(1,ℤ/8)D89
hypocenterC89C2×#2051
LCSG ▷ C22×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

1490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 197432);