Finite Group Databasebeta

D8×#6099 #15834342

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD8×#6099

Splittings

SylowC13 ⋊ M16×D8

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C4×C13×D8C2
socleC22×C13C2×C4×D4
prime radicalC22×C13×D8C4
cosocleC42×C13C24
hypercenterC2×C4×D8D13
hypocenterC13M16×D8
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D8

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 140991);