Finite Group Databasebeta

C2×#13068727 #14753636

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13068727

Splittings

SylowC11 ⋊ C2×#1829

Subgroups

subgroupG/H
centerC22#10622824
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#518C2
socleC22×C11#381
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC2×#518D11
hypocenterC11C2×#1829
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#518

1434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

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, 169431);