Finite Group Databasebeta

C2×C4×#901 #11658588

order768
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×#901

Splittings

FittingC22×C3×C4×C8 ⋊ C2
SylowC3 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC2×C4×C8C2×D3
commutatorC2×C3C23×C42
FrattiniC2×C4C24×D3
FittingC22×C3×C4×C8C2
socleC23×C3C23×C4
prime radicalC22×#235C22
cosocleC2×C3×C4C25
hypercenterC22×C4×C8D3
hypocenterC3C2×C4×#131
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C8 ◁ C22×C4×C8

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1032969);