Finite Group Databasebeta

D4×#10587680 #17979732

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD4×#10587680

Splittings

SylowC17 ⋊ D4×#131

Subgroups

subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingD4×Q8×C17C4
prime radicalD4×#63256C2
cosocleC2×Dic17C25
hypercenterD4×Q8#595
hypocenterC17D4×#131
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ D4×Q8

2814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114976);