Finite Group Databasebeta

#332×Dic19 #18073489

order4864
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#332×Dic19

Splittings

SylowC19 ⋊ C4×#332

Subgroups

subgroupG/H
centerC23C22⋊C4×D19
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC2×C19×#332C2
socle, prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenterC2×#332D19
hypocenterC19C4×#332
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4864

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 60518);