Finite Group Databasebeta

C22×#11758453 #16858967

order3968
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC22×#11758453

Splittings

FittingC22×C42×C31 ⋊ C2
SylowC31 ⋊ C22×#126

Subgroups

subgroupG/H
centerC24C22×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC22×C42×C31C2
socleC24×C31C23
prime radicalC24×D31C22
hypercenterC22×C42D31
hypocenterC31C22×#126
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C24 ◁ C22×C42

1320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

1016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 17766);