Finite Group Databasebeta

D4×#10587670 #17983159

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

Aliases

direct productD4×#10587670

Splittings

SylowC17 ⋊ D4×M32

Subgroups

subgroupG/H
center, FrattiniC22C23×#3633
commutator, socleC22×C17C23×C8
Fitting, prime radicalC22×D4×C17C8
cosocleC2×#3624C24
hypercenterC22×D4#3633
hypocenterC17D4×M32
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×D4

734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118403);