Finite Group Databasebeta

C2×#13077550 #15618138

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

Aliases

direct productC2×#13077550

Splittings

SylowC11 ⋊ C2×#2960

Subgroups

subgroupG/H
centerC22×C8C22×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC22×C4×C8×C11C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC2×C4×C11C25
hypercenterC22×C4×C8D11
hypocenterC11C2×#2960
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C8 ◁ C22×C4×C8

1982 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1033933);