Finite Group Databasebeta

C23×#66999 #15660413

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

Aliases

direct productC23×#66999

Splittings

FittingC24×Q8×C11 ⋊ C2
SylowC11 ⋊ C23×C22⋊Q8

Subgroups

subgroupG/H
centerC25C22×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC24×Q8×C11C2
socleC25×C11C23
prime radicalC25×D11C22
hypercenterC24×Q8D11
hypocenterC11C23×C22⋊Q8
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C25 ◁ C24×Q8

14078 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, 1076208);