Finite Group Databasebeta

C22×#11758405 #16854283

order3968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11758405

Splittings

SylowC31 ⋊ C22×#106

Subgroups

subgroupG/H
centerC24D124
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
FittingC23×C8×C31C2
socle, prime radicalC24×C31D4
cosocleC2×C4×C31C24
hypercenterC23×C8D31
hypocenterC31C22×#106
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

600 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, 13082);