Finite Group Databasebeta

#339×Dic19 #18087710

order4864
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct product#339×Dic19

Splittings

SylowC19 ⋊ C4×#339

Subgroups

subgroupG/H
centerC22×C4D4×D19
commutatorC4×C19C43
FrattiniC23×C4C22×D19
FittingC2×C19×#339C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC2×#339D19
hypocenterC19C4×#339
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

1214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 74739);