Finite Group Databasebeta

#1703×D83 #35386973

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct product#1703×D83

Splittings

FittingC83×#1703 ⋊ C2
SylowC83 ⋊ C2×#1703

Subgroups

subgroupG/H
centerC22#121×D83
commutator, cosocleC42×C83C24
FrattiniC42C23×D83
FittingC83×#1703C2
socleC22×C83C2×#121
prime radicalC2×D4×D83D4
hypercenter#1703D83
hypocenterC83C2×#1703
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #1703

694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 152137);