Finite Group Databasebeta

C23×#66977 #15660416

order2816
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC23×#66977

Splittings

SylowC11 ⋊ C23×C22⋊Q8

Subgroups

subgroupG/H
centerC25C22×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC25×C4×C11C2
socleC25×C11C23
prime radicalC26×C11C22
hypercenterC25×C4D11
hypocenterC11C23×C22⋊Q8
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C25 ◁ C25×C4

14078 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, 1076211);