Finite Group Databasebeta

#1367×D83 #35315944

order21248
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct product#1367×D83

Splittings

FittingC83×#1367 ⋊ C2
SylowC83 ⋊ C2×#1367

Subgroups

subgroupG/H
centerC2×C8D4×D83
commutatorC4×C83C22×C16
FrattiniC4×C8C22×D83
FittingC83×#1367C2
socleC22×C83C2×C4⋊C8
prime radicalC22×D83C4⋊C8
cosocleC4×C8×C83C23
hypercenter#1367D83
hypocenterC83C2×#1367
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ #1367

286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

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, 81108);