Finite Group Databasebeta

C2×#31771162 #46824176

order34432
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#31771162

Splittings

SylowC269 ⋊ C2×#533

Subgroups

subgroupG/H
centerC22×C4C22×D269
commutator, cosocleC22×C269C25
FrattiniC22C24×D269
FittingC22×C42×C269C2
socleC23×C269C24
prime radicalC24×C269C23
hypercenterC22×C42D269
hypocenterC269C2×#533
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C22×C4 ◁ C22×C42

1168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

8632 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 17801);