Finite Group Databasebeta

D4×Dic104 #16019649

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD4×Dic104

Splittings

SylowC13 ⋊ D4×Q32

Subgroups

subgroupG/H
centerC22C22×D104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingD4×C13×C16C2
socleC22×C13C22×D8
prime radicalC2×D4×C13D8
hypercenterD4×C16D13
hypocenterC13D4×Q32
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16

664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 326298);