Finite Group Databasebeta

D8×#63243 #17967721

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD8×#63243

Splittings

SylowC17 ⋊ M16×D8

Subgroups

subgroupG/H
centerC22C2×D4×#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC4×D8×C17C4
socleC22×C17C2×C4×D4
prime radicalC2×D8×D17C4
cosocleC4×Dic17C24
hypercenterC4×D8#595
hypocenterC17M16×D8
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1102965);