Finite Group Databasebeta

C4×#11763653 #17951756

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#11763653

Splittings

SylowC17 ⋊ C4×#323

Subgroups

subgroupG/H
centerC22×C4C22⋊#595
commutatorC22×C17C2×C4×C8
FrattiniC24C22×#595
FittingC22×C42×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17C2×C4
cosocleC23×Dic17C23
hypercenterC22×C42#595
hypocenterC17C4×#323
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1087000);