Finite Group Databasebeta

D4×C22⋊C4×D13 #16022086

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productD4×C22⋊C4×D13

Splittings

FittingD4×C13×C22⋊C4 ⋊ C2
SylowC13 ⋊ C2×D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingD4×C13×C22⋊C4C2
socle, cosocleC23×C13C25
prime radicalC23×D4×D13C2
hypercenterD4×C22⋊C4D13
hypocenterC13C2×D4×C22⋊C4
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ D4×C22⋊C4

8774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 328735);