Finite Group Databasebeta

C23×#66932 #15660443

order2816
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC23×#66932

Splittings

SylowC11 ⋊ C23×#126

Subgroups

subgroupG/H
centerC25C22×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC23×C11×C22⋊C4C2
socleC25×C11C23
prime radicalC26×C11C22
hypercenterC23×C22⋊C4D11
hypocenterC11C23×#126
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C25 ◁ C23×C22⋊C4

9486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076238);