Finite Group Databasebeta

#562×Dic17 #17197024

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

Aliases

direct product#562×Dic17

Splittings

SylowC17 ⋊ C4×#562

Subgroups

subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
Fitting, prime radicalC2×C17×#562C2
socle, cosocleC23×C17C25
hypercenterC2×#562D17
hypocenterC17C4×#562
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#562

2248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 332268);