Finite Group Databasebeta

C4×#11718667 #15860571

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

Aliases

direct productC4×#11718667

Splittings

FittingC4×C13×#117 ⋊ C2
SylowC13 ⋊ C4×#410

Subgroups

subgroupG/H
centerC42#6103
commutatorC22×C13C22×C42
FrattiniC24C23×D13
FittingC4×C13×#117C2
socleC22×C13C22×C22⋊C4
prime radicalC22×#6127C22
cosocleC24×C13C24
hypercenterC4×#117D13
hypocenterC13C4×#410
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C22×C42 ◁ C4×#117

1666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 167220);