Finite Group Databasebeta

C22⋊Q8×#1055 #15870334

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22⋊Q8×#1055

Splittings

SylowC13 ⋊ C8×C22⋊Q8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C23×C8
FittingC4×C13×C22⋊Q8C2
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenterC4×C22⋊Q8D13
hypocenterC13C8×C22⋊Q8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 176983);