Finite Group Databasebeta

C22×#11758478 #16860415

order3968
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11758478

Splittings

FittingC23×C8×C31 ⋊ C2
SylowC31 ⋊ C22×#131

Subgroups

subgroupG/H
centerC22×C8C2×D31
commutatorC2×C31C24×C4
FrattiniC4C24×D31
FittingC23×C8×C31C2
socleC23×C31C22×C4
prime radicalC22×#92495C2
cosocleC4×C31C25
hypercenterC23×C8D31
hypocenterC31C22×#131
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22×C8 ◁ C23×C8

1504 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, 19214);