Finite Group Databasebeta

D4×#10587538 #17978560

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productD4×#10587538

Splittings

SylowC17 ⋊ D4×M32

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×#595
commutator, socleC22×C17C23×C8
FittingC2×C4×D4×C17C4
prime radicalC22×D4×C17C8
cosocleC2×#3622C24
hypercenterC2×C4×D4#595
hypocenterC17D4×M32
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113804);