Finite Group Databasebeta

D4×#88121 #16803045

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#88121

Splittings

SylowC13 ⋊ D4×#100

Subgroups

subgroupG/H
centerC22C22×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC23×D4×C13C4
socleC22×C13C22×C22⋊C4
prime radicalC2×D4×C22⋊D13C2
cosocleC22×Dic13C24
hypercenterC23×D4#261
hypocenterC13D4×#100
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×D4 ◁ C23×D4

1862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1109694);