Finite Group Databasebeta

C2×C8×C22⋊D31 #16854382

order3968
isoclinismisoclinic class of Dic62
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×C8×C22⋊D31

Splittings

FittingC23×C8×C31 ⋊ C2
SylowC31 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C8C2×D31
commutatorC2×C31C23×C8
FrattiniC2×C4C23×D31
FittingC23×C8×C31C2
socleC23×C31C22×C4
prime radicalC22×C22⋊D31C4
cosocleC2×C4×C31C24
hypercenterC23×C8D31
hypocenterC31C2×C8×D4
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22×C8 ◁ C23×C8

616 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, 13181);