Finite Group Databasebeta

C2×#13077095 #15617268

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

Aliases

direct productC2×#13077095

Splittings

SylowC11 ⋊ C2×#2888

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
Fitting, prime radicalC22×C11×H(5,𝔽2)C2
socleC22×C11C22×C22⋊C4
cosocleC2×C4×C11C25
hypercenterC22×H(5,𝔽2)D11
hypocenterC11C2×#2888
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ C22×H(5,𝔽2)

5114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

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, 1033063);