Finite Group Databasebeta

C2×#13071414 #14912676

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13071414

Splittings

SylowC11 ⋊ C2×#2336

Subgroups

subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#389C2
socle, prime radicalC24×C11C24
cosocleC23×C11C25
hypercenterC2×#389D11
hypocenterC11C2×#2336
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

2310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 328471);