Finite Group Databasebeta

#559×Dic17 #17194313

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

Aliases

direct product#559×Dic17

Splittings

SylowC17 ⋊ C4×#559

Subgroups

subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC2×C17×#559C2
socle, cosocleC23×C17C25
prime radicalC2×C17×#127C22
hypercenterC2×#559D17
hypocenterC17C4×#559
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#559

2564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 329557);