Finite Group Databasebeta

C8×#66867 #14643126

order2816
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct productC8×#66867

Splittings

SylowC11 ⋊ C8×#97

Subgroups

subgroupG/H
centerC2×C4×C8C2×D11
commutatorC2×C11C42×C8
FrattiniC2×C42C22×D11
FittingC42×C8×C11C2
socle, prime radicalC23×C11C2×C42
cosocleC2×C42×C11C23
hypercenterC42×C8D11
hypocenterC11C8×#97
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4×C8 ◁ C42×C8

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

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, 58921);