Finite Group Databasebeta

C2×#13077636 #15618275

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

Aliases

direct productC2×#13077636

Splittings

SylowC11 ⋊ C2×#2971

Subgroups

subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C4×C11×#41C2
socleC23×C11C23×C4
prime radicalC22×C11×#41C4
cosocleC2×C4×C11C25
hypercenterC2×C4×#41D11
hypocenterC11C2×#2971
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

2230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1034070);