Finite Group Databasebeta

C2×#13077995 #15620435

order2816
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13077995

Splittings

SylowC11 ⋊ C2×#3022

Subgroups

subgroupG/H
centerC22C2×#67006
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#585C2
socleC22×C11C2×#120
hypercenterC2×#585D11
hypocenterC11C2×#3022
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#585

4742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1036230);