Finite Group Databasebeta

C4×#11763780 #17968292

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#11763780

Splittings

SylowC17 ⋊ C4×#407

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC22×C17C22×C42
FrattiniC23C23×#595
FittingC22×C42×C17C4
socleC23×C17C23×C4
prime radicalC24×D17C2×C4
cosocleC22×Dic17C24
hypercenterC22×C42#595
hypocenterC17C4×#407
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42

2246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103536);