Finite Group Databasebeta

C2×#13077080 #15617247

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13077080

Splittings

SylowC11 ⋊ C2×#2884

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
Fitting, prime radicalC22×C11×2−1+4C2
socleC22×C11C22×C22⋊C4
cosocleC23×C11C25
hypercenterC22×2−1+4D11
hypocenterC11C2×#2884
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×Q8 ◁ C22×2−1+4

4818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1033042);