Finite Group Databasebeta

C2×#131×Dic83 #36267806

order21248
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#131×Dic83

Splittings

SylowC83 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC22×C8C22×D83
commutatorC2×C83C23×C42
FrattiniC2×C4C24×D83
FittingC22×#131×C83C2
socleC23×C83C23×C4
prime radicalC22×#41×C83C22
cosocleC2×C4×C83C25
hypercenterC22×#131D83
hypocenterC83C2×C4×#131
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C8 ◁ C22×#131

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1032970);