Finite Group Databasebeta

C4×D8×D31 #16854458

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

Aliases

direct productC4×D8×D31

Splittings

FittingC4×D8×C31 ⋊ C2
SylowC31 ⋊ C2×C4×D8

Subgroups

subgroupG/H
centerC2×C4D4×D31
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
FittingC4×D8×C31C2
socleC22×C31C22×D4
prime radicalC2×D8×D31C2
cosocleC2×C4×C31C24
hypercenterC4×D8D31
hypocenterC31C2×C4×D8
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 992

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 13257);