Finite Group Databasebeta

C22×C4×#4318 #15617161

order2816
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×C4×#4318

Splittings

SylowC11 ⋊ C22×C4×M16

Subgroups

subgroupG/H
centerC22×C42C2×D11
commutatorC2×C11C23×C42
FrattiniC2×C4C24×D11
FittingC23×C42×C11C2
socleC24×C11C22×C4
prime radicalC25×C11C2×C4
cosocleC2×C4×C11C25
hypercenterC23×C42D11
hypocenterC11C22×C4×M16
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C42 ◁ C23×C42

3950 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, 1032956);