Finite Group Databasebeta

C8×D4×#261 #16797335

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC8×D4×#261

Splittings

FittingC8×D4×C13 ⋊ C4
SylowC13 ⋊ C4×C8×D4

Subgroups

subgroupG/H
centerC2×C8C22×#261
commutatorC2×C13C22×C4×C8
FrattiniC2×C4C23×#261
FittingC8×D4×C13C4
socleC22×C13C22×C42
prime radicalC2×D4×D13C2×C4
cosocleC2×C4×D13C24
hypercenterC8×D4#261
hypocenterC13C4×C8×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C8×D4

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103984);