Finite Group Databasebeta

C22×D13×C22⋊Q8 #16769558

order3328
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×D13×C22⋊Q8

Splittings

FittingC22×C13×C22⋊Q8 ⋊ C2
SylowC13 ⋊ C23×C22⋊Q8

Subgroups

subgroupG/H
centerC24C23×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC22×C13×C22⋊Q8C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC22×C22⋊Q8D13
hypocenterC13C23×C22⋊Q8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

14078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076207);