Finite Group Databasebeta

#568×Dic17 #17897738

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct product#568×Dic17

Splittings

SylowC17 ⋊ C4×#568

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D17
commutatorC2×C17C23×C42
FittingC2×C17×#568C2
socleC22×C17C24×C4
prime radicalC22×#41×C17C22
cosocleC2×C4×C17C25
hypercenterC2×#568D17
hypocenterC17C4×#568
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×#568

3250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1032982);