Finite Group Databasebeta

C22×C4×#4339 #15660347

order2816
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×C4×#4339

Splittings

FittingC23×C42×C11 ⋊ C2
SylowC11 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC22×C42C2×D11
commutatorC2×C11C25×C4
FrattiniC22C25×D11
FittingC23×C42×C11C2
socleC24×C11C24
prime radicalC23×#4339C2
cosocleC22×C11C26
hypercenterC23×C42D11
hypocenterC11C22×C4×#41
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C42 ◁ C23×C42

12878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076142);