Finite Group Databasebeta

C4×#11718449 #15861386

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

Aliases

direct productC4×#11718449

Splittings

FittingC4×C13×#103 ⋊ C2
SylowC13 ⋊ C42×SD16

Subgroups

subgroupG/H
centerC22×C4D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC4×C13×#103C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenterC4×#103D13
hypocenterC13C42×SD16
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

1230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 168035);