Finite Group Databasebeta

#339×Dic83 #35309575

order21248
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct product#339×Dic83

Splittings

SylowC83 ⋊ C4×#339

Subgroups

subgroupG/H
centerC22×C4D4×D83
commutatorC4×C83C43
FrattiniC23×C4C22×D83
FittingC2×#339×C83C2
socleC23×C83C2×C22⋊C4
prime radicalC24×C83C2×D4
cosocleC23×C4×C83C23
hypercenterC2×#339D83
hypocenterC83C4×#339
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

1214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 74739);