Finite Group Databasebeta

#2138×D83 #35557282

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#2138×D83

Splittings

FittingC83×#2138 ⋊ C2
SylowC83 ⋊ C2×#2138

Subgroups

subgroupG/H
centerC2×C4D8×D83
commutatorC8×C83C23×C4
FrattiniC2×C8C23×D83
FittingC83×#2138C2
socleC22×C83C22×D8
prime radicalC2×#135×D83C2
cosocleC2×C8×C83C24
hypercenter#2138D83
hypocenterC83C2×#2138
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2138

1190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 322446);