Finite Group Databasebeta

C4×#11718371 #15861415

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#11718371

Splittings

FittingC4×C13×#97 ⋊ C2
SylowC13 ⋊ C4×#440

Subgroups

subgroupG/H
centerC22×C4C2×D52
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC4×C13×#97C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenterC4×#97D13
hypocenterC13C4×#440
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#97

1206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 168064);