Finite Group Databasebeta

#518×Dic17 #17192560

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct product#518×Dic17

Splittings

SylowC17 ⋊ C4×#518

Subgroups

subgroupG/H
center, FrattiniC23C24×D17
commutatorC2×C17C23×C42
FittingC2×C17×#518C2
socle, cosocleC23×C17C25
prime radicalC23×D4×C17C22
hypercenterC2×#518D17
hypocenterC17C4×#518
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#518

4186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327804);