Finite Group Databasebeta

C22×#19099203 #35195191

order20224
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×#19099203

Splittings

FittingC23×C22⋊C4×C79 ⋊ C2
SylowC79 ⋊ C22×#546

Subgroups

subgroupG/H
centerC24C23×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC23×C22⋊C4×C79C2
socleC24×C79C24
hypercenterC23×C22⋊C4D79
hypocenterC79C22×#546
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C23×C22⋊C4

14462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

3220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 1076490);