Finite Group Databasebeta

D4×(C2×#261)⋊C4 #16791636

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productD4×(C2×#261)⋊C4

Splittings

FittingC2×C4×D4×C13 ⋊ C4
SylowC13 ⋊ D4×#95

Subgroups

subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC2×C4×D4×C13C4
socleC23×C13C23×C4
prime radicalC22×D4×D13C22
cosocleC23×D13C24
hypercenterC2×C4×D4#261
hypocenterC13D4×#95
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4

3562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 1098285);