Finite Group Databasebeta

C4×#11719320 #16022018

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#11719320

Splittings

FittingC4×C13×#121 ⋊ C2
SylowC13 ⋊ C4×#540

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC4×C13×#121C2
socle, cosocleC23×C13C25
prime radicalC2×#11719320C2
hypercenterC4×#121D13
hypocenterC13C4×#540
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×#121

2518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 328667);