Finite Group Databasebeta

C2×C16×Dic22 #14907254

order2816
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×C16×Dic22

Splittings

SylowC11 ⋊ C2×Q8×C16

Subgroups

subgroupG/H
centerC22×C16C2×D11
commutatorC2×C11C23×C16
FrattiniC2×C8C23×D11
FittingC2×C4×C11×C16C2
socle, prime radicalC23×C11C22×C8
cosocleC2×C8×C11C24
hypercenterC2×C4×C16D11
hypocenterC11C2×Q8×C16
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C16 ◁ C2×C4×C16

582 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, 323049);