Finite Group Databasebeta

D4×#88110 #16797400

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productD4×#88110

Splittings

SylowC13 ⋊ D4×#97

Subgroups

subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC2×C4×D4×C13C4
socleC23×C13C23×C4
prime radicalC22×D4×C13C2×C4
cosocleC22×Dic13C24
hypercenterC2×C4×D4#261
hypocenterC13D4×#97
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4

1274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1104049);