Finite Group Databasebeta

C2×#31770533 #46814112

order34432
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#31770533

Splittings

SylowC269 ⋊ C2×#397

Subgroups

subgroupG/H
centerC24C22×D269
commutator, cosocleC23×C269C24
FrattiniC23C23×D269
FittingC22×C22⋊C4×C269C2
socleC24×C269C23
prime radicalC25×C269C22
hypercenterC22×C22⋊C4D269
hypocenterC269C2×#397
LCSG ▷ C23×C269 ▷ C269
UCSC1 ◁ C24 ◁ C22×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

5404 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 7737);