Finite Group Databasebeta

#2179×D83 #35557806

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#2179×D83

Splittings

FittingC83×#2179 ⋊ C2
SylowC83 ⋊ C2×#2179

Subgroups

subgroupG/H
centerC4C2×D8×D83
commutatorC8×C83C23×C4
FrattiniC2×C8C23×D83
FittingC83×#2179C2
socleC2×C83C2×C4×D8
prime radical#508×D83C2
cosocleC2×C8×C83C24
hypercenter#2179D83
hypocenterC83C2×#2179
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8 ◁ #2179

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 322970);