Finite Group Databasebeta

C2×D1016 #16861220

order4064
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×D1016

Splittings

FittingC2×C8×C127 ⋊ C2
SylowC127 ⋊ C2×D8

Subgroups

subgroupG/H
centerC22D508
commutator, cosocleC4×C127C23
FrattiniC4C22×D127
FittingC2×C8×C127C2
socleC22×C127D4
hypercenterC2×C8D127
hypocenterC127C2×D8
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2032

Conjugacy classes & character table

1022 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4064, 157);