Finite Group Databasebeta

#346×Dic17 #16949144

order4352
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct product#346×Dic17

Splittings

SylowC17 ⋊ C4×#346

Subgroups

subgroupG/H
center, FrattiniC22×C8C22×D17
commutatorC2×C17C42×C8
FittingC2×C17×#346C2
socle, prime radicalC23×C17C22×C8
cosocleC22×C8×C17C23
hypercenterC2×#346D17
hypocenterC17C4×#346
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C2×#346

510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84388);