Finite Group Databasebeta

#1302×D83 #35294658

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct product#1302×D83

Splittings

FittingC83×#1302 ⋊ C2
SylowC83 ⋊ C2×#1302

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D83
commutatorC2×C4×C83C2×C42
FrattiniC2×C42C22×D83
FittingC83×#1302C2
socleC22×C83C2×#95
prime radicalC23×D83C4⋊C4
cosocleC2×C42×C83C23
hypercenter#1302D83
hypocenterC83C2×#1302
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1302

642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1634 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 59822);