Finite Group Databasebeta

#376×Dic17 #16955395

order4352
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C44

Aliases

direct product#376×Dic17

Splittings

SylowC17 ⋊ C4×#376

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC2×C17C2×C43
FrattiniC24C23×D17
FittingC2×C17×#376C2
socle, prime radical, cosocleC24×C17C24
hypercenterC2×#376D17
hypocenterC17C4×#376
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C2×#376

2302 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, 90639);