Finite Group Databasebeta

C2×#31771441 #46825693

order34432
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC2×#31771441

Splittings

FittingC22×#41×C269 ⋊ C2
SylowC269 ⋊ C2×#585

Subgroups

subgroupG/H
centerC2×C4C23×D269
commutator, cosocleC2×C269C26
FrattiniC2C25×D269
FittingC22×#41×C269C2
socleC22×C269C25
hypercenterC22×#41D269
hypocenterC269C2×#585
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ C22×#41

5956 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8608

Conjugacy classes & character table

5428 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 19318);