Finite Group Databasebeta

#389×Dic17 #16955520

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct product#389×Dic17

Splittings

SylowC17 ⋊ C4×#389

Subgroups

subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC2×C17×#389C2
socle, prime radical, cosocleC24×C17C24
hypercenterC2×#389D17
hypocenterC17C4×#389
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#389

1918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

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, 90764);