Finite Group Databasebeta

C4×#11718304 #16789309

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#11718304

Splittings

SylowC13 ⋊ C4×#350

Subgroups

subgroupG/H
centerC42C22⋊#261
commutatorC4×C13C2×C4×C8
FrattiniC22×C4C22×#261
FittingC4×C13×#41C4
socleC22×C13C2×C22⋊C8
prime radicalC2×C13×#41C2×C4
cosocleC22×#1055C23
hypercenterC4×#41#261
hypocenterC13C4×#350
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#41

490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1095958);