Finite Group Databasebeta

C22⋊Q8×#89137 #28379498

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22⋊Q8×#89137

Splittings

FittingC22⋊Q8×C109 ⋊ C4
SylowC109 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
center, FrattiniC22C23×#89137
commutator, socleC22×C109C23×C4
FittingC22⋊Q8×C109C4
prime radicalC23×D109C23
cosocleC22×D109C24
hypercenterC22⋊Q8#89137
hypocenterC109C4×C22⋊Q8
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22⋊Q8

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20976);