Finite Group Databasebeta

D4×#10587553 #17974450

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#10587553

Splittings

SylowC17 ⋊ D4×#100

Subgroups

subgroupG/H
centerC22C22×C22⋊#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC23×D4×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC2×D4×C22⋊D17C2
cosocleC22×Dic17C24
hypercenterC23×D4#595
hypocenterC17D4×#100
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×D4 ◁ C23×D4

1862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

215 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1109694);