Finite Group Databasebeta

#352×Dic17 #16949463

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#352×Dic17

Splittings

SylowC17 ⋊ C4×#352

Subgroups

subgroupG/H
centerC22#99×D17
commutatorC23×C17C2×C42
FrattiniC22×D4C22×D17
FittingC2×C17×#352C2
socleC22×C17C2×#99
prime radical, cosocleC22×D4×C17C23
hypercenterC2×#352D17
hypocenterC17C4×#352
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

576 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, 84707);