Finite Group Databasebeta

C2×D8504 #46801206

order34016
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×D8504

Splittings

FittingC2×C8×C1063 ⋊ C2
SylowC1063 ⋊ C2×D8

Subgroups

subgroupG/H
centerC22D4252
commutator, cosocleC4×C1063C23
FrattiniC4C22×D1063
FittingC2×C8×C1063C2
socleC22×C1063D4
hypercenterC2×C8D1063
hypocenterC1063C2×D8
LCSG ▷ C4×C1063 ▷ C2×C1063 ▷ C1063
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17008

Conjugacy classes & character table

8510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34016, 157);