Finite Group Databasebeta

#2117×D83 #35557103

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

Aliases

direct product#2117×D83

Splittings

FittingC83×#2117 ⋊ C2
SylowC83 ⋊ C2×#2117

Subgroups

subgroupG/H
centerC8C2×D4×D83
commutatorC4×C83C23×C8
FrattiniC2×C8C23×D83
FittingC83×#2117C2
socleC2×C83C22×C22⋊C8
prime radicalC2×#41×D83C4
cosocleC2×C8×C83C24
hypercenter#2117D83
hypocenterC83C2×#2117
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2117

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

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, 322267);