Finite Group Databasebeta

#366×Dic83 #35319805

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#366×Dic83

Splittings

SylowC83 ⋊ C4×#366

Subgroups

subgroupG/H
centerC23D8×D83
commutatorC8×C83C2×C42
FrattiniC22×C8C22×D83
FittingC2×#366×C83C2
socle, prime radicalC23×C83C2×D8
cosocleC22×C8×C83C23
hypercenterC2×#366D83
hypocenterC83C4×#366
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#366

366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

1892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 84969);