Finite Group Databasebeta

#2113×D83 #35557074

order21248
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct product#2113×D83

Splittings

FittingC83×#2113 ⋊ C2
SylowC83 ⋊ C2×#2113

Subgroups

subgroupG/H
center, FrattiniC2×C8C23×D83
commutator, socleC22×C83C23×C8
FittingC83×#2113C2
prime radicalC2×#41×D83C4
cosocleC2×C8×C83C24
hypercenter#2113D83
hypocenterC83C2×#2113
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C8 ◁ #2113

1190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 322238);