Finite Group Databasebeta

#2078×D83 #35433293

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#2078×D83

Splittings

FittingC83×#2078 ⋊ C2
SylowC83 ⋊ C2×#2078

Subgroups

subgroupG/H
centerC22#121×D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2078C2
socleC22×C83C2×#121
prime radicalC2×#41×D83C22
hypercenter#2078D83
hypocenterC83C2×#2078
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2078

950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 198457);