Finite Group Databasebeta

C2×#13070722 #14908223

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13070722

Splittings

SylowC11 ⋊ C2×#2219

Subgroups

subgroupG/H
centerC23C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#467C2
socleC23×C11C2×D8
prime radicalC24×C11D8
hypercenterC2×#467D11
hypocenterC11C2×#2219
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 324018);