Finite Group Databasebeta

#339×Dic17 #16939495

order4352
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct product#339×Dic17

Splittings

SylowC17 ⋊ C4×#339

Subgroups

subgroupG/H
centerC22×C4D4×D17
commutatorC4×C17C43
FrattiniC23×C4C22×D17
FittingC2×C17×#339C2
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenterC2×#339D17
hypocenterC17C4×#339
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

1214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 74739);