Finite Group Databasebeta

#344×Dic19 #18087746

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

Aliases

direct product#344×Dic19

Splittings

SylowC19 ⋊ C4×#344

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D19
commutatorC22×C19C43
FrattiniC23×C4C22×D19
FittingC2×C19×#344C2
socleC22×C19C2×#95
prime radicalC24×C19C22×C4
cosocleC23×C4×C19C23
hypercenterC2×#344D19
hypocenterC19C4×#344
LCSG ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 74775);