Finite Group Databasebeta

#1580×D83 #35373799

order21248
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct product#1580×D83

Splittings

FittingC83×#1580 ⋊ C2
SylowC83 ⋊ C2×#1580

Subgroups

subgroupG/H
centerC2×C4C2×D4×D83
commutatorC4×C83C23×C8
FrattiniC42C23×D83
FittingC83×#1580C2
socleC22×C83C2×C4×D4
prime radicalC2×D8×D83C4
cosocleC42×C83C24
hypercenter#1580D83
hypocenterC83C2×#1580
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

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, 138963);