Finite Group Databasebeta

D8×D1051 #46777688

order33632
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD8×D1051

Splittings

FittingD8×C1051 ⋊ C2
SylowC1051 ⋊ C2×D8

Subgroups

subgroupG/H
centerC2D4×D1051
commutator, cosocleC4×C1051C23
FrattiniC4C22×D1051
FittingD8×C1051C2
socleC2×C1051C2×D4
hypercenterD8D1051
hypocenterC1051C2×D8
LCSG ▷ C4×C1051 ▷ C2×C1051 ▷ C1051
UCSC1 ◁ C2 ◁ C4 ◁ D8

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8408

Conjugacy classes & character table

3689 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33632, 155);