Finite Group Databasebeta

C22×#19098454 #34446596

order20224
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×#19098454

Splittings

FittingC23×C42×C79 ⋊ C2
SylowC79 ⋊ C22×#388

Subgroups

subgroupG/H
centerC25C22×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC23×C42×C79C2
socleC25×C79C23
prime radicalC25×D79C22
cosocleC23×C79C25
hypercenterC23×C42D79
hypocenterC79C22×#388
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C25 ◁ C23×C42

5966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

5104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 327895);