Finite Group Databasebeta

C2×#30686021 #46803604

order34208
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30686021

Splittings

FittingC2×C8×C1069 ⋊ C2
SylowC1069 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22D4276
commutator, cosocleC4×C1069C23
FrattiniC4C22×D1069
FittingC2×C8×C1069C2
socleC22×C1069D4
prime radicalC2×D4276C2
hypercenterC2×C8D1069
hypocenterC1069C2×SD16
LCSG ▷ C4×C1069 ▷ C2×C1069 ▷ C1069
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17104

Conjugacy classes & character table

8558 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34208, 161);