Finite Group Databasebeta

C4×#11763675 #17956578

order4352
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#11763675

Splittings

SylowC17 ⋊ C4×#336

Subgroups

subgroupG/H
centerC23×C4C2×#595
commutatorC2×C17C42×C8
FrattiniC24C22×#595
FittingC22×C42×C17C4
socle, prime radicalC24×C17C22×C4
cosocleC23×Dic17C23
hypercenterC22×C42#595
hypocenterC17C4×#336
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×C42

1318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1091822);