Finite Group Databasebeta

C2×C4×(C2×D31)⋊C4 #16848042

order3968
isoclinismisoclinic class of Dic62
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D31)⋊C4

Splittings

FittingC22×C42×C31 ⋊ C2
SylowC31 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D31
commutatorC2×C31C22×C42
FrattiniC23C23×D31
FittingC22×C42×C31C2
socleC24×C31C23
prime radicalC24×D31C22
cosocleC23×C31C24
hypercenterC22×C42D31
hypocenterC31C2×C4×C22⋊C4
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 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, 6841);