Finite Group Databasebeta

#564×Dic17 #17197046

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#564×Dic17

Splittings

SylowC17 ⋊ C4×#564

Subgroups

subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC2×C17×#564C2
socle, prime radical, cosocleC23×C17C25
hypercenterC2×#564D17
hypocenterC17C4×#564
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#564

1800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 332290);