Finite Group Databasebeta

#1796×D83 #35403741

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct product#1796×D83

Splittings

FittingC83×#1796 ⋊ C2
SylowC83 ⋊ C2×#1796

Subgroups

subgroupG/H
centerC2#379×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1796C2
socleC2×C83C2×#379
prime radicalC2×2−1+4×D83C2
cosocleC22×C4×C83C24
hypercenter#1796D83
hypocenterC83C2×#1796
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1796

3602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

1247 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 168905);