Finite Group Databasebeta

C2×#13066857 #14675431

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13066857

Splittings

SylowC11 ⋊ C2×#1438

Subgroups

subgroupG/H
centerC25C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
Fitting, prime radicalC24×D4×C11C2
socleC25×C11C23
cosocleC24×C11C24
hypercenterC24×D4D11
hypocenterC11C2×#1438
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C25 ◁ C24×D4

8190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 91226);