Finite Group Databasebeta

C2×#26021522 #36582255

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

Aliases

direct productC2×#26021522

Splittings

SylowC89 ⋊ C2×#2048

Subgroups

subgroupG/H
centerC22#19151512
commutator, cosocleC22×C4×C89C24
FrattiniC22×C4C23×D89
Fitting, prime radicalC22×AGL(1,ℤ/8)×C89C2
socleC22×C89#394
hypercenterC22×AGL(1,ℤ/8)D89
hypocenterC89C2×#2048
LCSG ▷ C22×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

1450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2848

Conjugacy classes & character table

1982 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 197395);