Finite Group Databasebeta

#340×Dic19 #18087718

order4864
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct product#340×Dic19

Splittings

SylowC19 ⋊ C4×#340

Subgroups

subgroupG/H
centerC24D4×D19
commutatorC4×C19C43
FrattiniC23×C4C22×D19
FittingC2×C19×#340C2
socle, prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC2×#340D19
hypocenterC19C4×#340
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4864

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, 74747);