Finite Group Databasebeta

C22×#11758391 #16854115

order3968
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11758391

Splittings

SylowC31 ⋊ C22×#97

Subgroups

subgroupG/H
centerC23×C4C2×D31
commutatorC2×C31C22×C42
FrattiniC2×C4C23×D31
FittingC22×C42×C31C2
socle, prime radicalC24×C31C2×C4
cosocleC2×C4×C31C24
hypercenterC22×C42D31
hypocenterC31C22×#97
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C23×C4 ◁ C22×C42

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3968

Conjugacy classes & character table

1040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 12914);