Finite Group Databasebeta

C2×#13066813 #14674262

order2816
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13066813

Splittings

SylowC11 ⋊ C2×#1422

Subgroups

subgroupG/H
centerC2×C16C22⋊D11
commutatorC4×C11C22×C16
FrattiniC2×C16C22×D11
FittingC2×C11×M64C2
socleC22×C11C4⋊C16
prime radicalC23×C11M32
cosocleC2×C11×C16C23
hypercenterC2×M64D11
hypocenterC11C2×#1422
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C16 ◁ C22×C16 ◁ C2×M64

214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 90057);