Finite Group Databasebeta

#340×Dic17 #16939503

order4352
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct product#340×Dic17

Splittings

SylowC17 ⋊ C4×#340

Subgroups

subgroupG/H
centerC24D4×D17
commutatorC4×C17C43
FrattiniC23×C4C22×D17
FittingC2×C17×#340C2
socle, prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenterC2×#340D17
hypocenterC17C4×#340
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

1182 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, 74747);