Finite Group Databasebeta

#1335×D83 #35314185

order21248
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct product#1335×D83

Splittings

FittingC83×#1335 ⋊ C2
SylowC83 ⋊ C2×#1335

Subgroups

subgroupG/H
centerC8D8×D83
commutatorC8×C83C22×C8
FrattiniC4×C8C22×D83
FittingC83×#1335C2
socleC2×C83C2×D4⋊C8
prime radical#135×D83C4
cosocleC4×C8×C83C23
hypercenter#1335D83
hypocenterC83C2×#1335
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C8 ◁ C2×C8 ◁ C4×C8 ◁ #1335

414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1328

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, 79349);