Finite Group Databasebeta

C2×#31771332 #46824456

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

Aliases

direct productC2×#31771332

Splittings

SylowC269 ⋊ C2×#557

Subgroups

subgroupG/H
centerC23C23×D269
commutator, cosocleC22×C269C25
FrattiniC22C24×D269
FittingC2×#125×C269C2
socle, prime radicalC23×C269C24
hypercenterC2×#125D269
hypocenterC269C2×#557
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ C2×#125

1048 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34432

Conjugacy classes & character table

3802 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 18081);