Finite Group Databasebeta

C2×#26018139 #36444567

order22784
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#26018139

Splittings

SylowC89 ⋊ C2×#1298

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic89
commutatorC2×C4×C89C2×C42
FrattiniC23×C4C22×D89
FittingC2×#407×C89C2
socleC23×C89#95
prime radicalC25×C89Q8
cosocleC23×C4×C89C23
hypercenterC2×#407D89
hypocenterC89C2×#1298
LCSG ▷ C2×C4×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×#407

938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

2540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 59707);