Finite Group Databasebeta

C22×C4×#235 #11701761

order768
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×C4×#235

Splittings

FittingC23×C3×C42 ⋊ C2
SylowC3 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC22×C42C2×D3
commutatorC2×C3C25×C4
FrattiniC22C25×D3
FittingC23×C3×C42C2
socleC24×C3C24
prime radicalC23×#235C2
cosocleC22×C3C26
hypercenterC23×C42D3
hypocenterC3C22×C4×#41
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C42 ◁ C23×C42

12878 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, 1076142);