Finite Group Databasebeta

C22×#11758400 #16858807

order3968
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11758400

Splittings

SylowC31 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C8C2×D31
commutatorC2×C31C23×C8
FrattiniC8C23×D31
FittingC23×C8×C31C2
socleC23×C31C2×C8
prime radicalC24×C31C8
cosocleC8×C31C24
hypercenterC23×C8D31
hypocenterC31C22×M32
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22×C8 ◁ C23×C8

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

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, 17606);