Finite Group Databasebeta

C22×#11758446 #16858987

order3968
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11758446

Splittings

SylowC31 ⋊ C22×C4⋊Q8

Subgroups

subgroupG/H
centerC24C22×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC22×C42×C31C2
socle, prime radicalC24×C31C23
hypercenterC22×C42D31
hypocenterC31C22×C4⋊Q8
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C24 ◁ C22×C42

1624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3968

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, 17786);