Finite Group Databasebeta

#2194×D83 #35558331

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct product#2194×D83

Splittings

FittingC83×#2194 ⋊ C2
SylowC83 ⋊ C2×#2194

Subgroups

subgroupG/H
centerC2#447×D83
commutator, cosocleC2×C8×C83C24
FrattiniC2×C8C23×D83
FittingC83×#2194C2
socleC2×C83C2×#447
prime radical#576×D83C2
hypercenter#2194D83
hypocenterC83C2×#2194
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #2194

1130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

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, 323495);