Finite Group Databasebeta

C2×#26018490 #36475564

order22784
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#26018490

Splittings

FittingC23×C42×C89 ⋊ C2
SylowC89 ⋊ C2×#1437

Subgroups

subgroupG/H
centerC25C22×D89
commutatorC22×C89C22×C42
FrattiniC24C23×D89
FittingC23×C42×C89C2
socleC25×C89C23
prime radicalC25×D89C22
cosocleC24×C89C24
hypercenterC23×C42D89
hypocenterC89C2×#1437
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C25 ◁ C23×C42

5230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11392

Conjugacy classes & character table

5744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 90704);