Finite Group Databasebeta

C8×#92497 #16854666

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

Aliases

direct productC8×#92497

Splittings

FittingC8×D4×C31 ⋊ C2
SylowC31 ⋊ C8×#41

Subgroups

subgroupG/H
centerC2×C8C22×D31
commutatorC2×C31C23×C8
FrattiniC2×C4C23×D31
FittingC8×D4×C31C2
socleC22×C31C23×C4
prime radicalC2×#92497C4
cosocleC2×C4×C31C24
hypercenterC8×D4D31
hypocenterC31C8×#41
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C8 ◁ C8×D4

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 13465);