Finite Group Databasebeta

C2×#31770589 #46819360

order34432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#31770589

Splittings

SylowC269 ⋊ C2×#413

Subgroups

subgroupG/H
centerC2×C4C22⋊Dic269
commutatorC22×C269C23×C4
FrattiniC2×C4C23×D269
Fitting, prime radicalC22×#41×C269C2
socleC22×C269C2×C22⋊C4
cosocleC2×C4×C269C24
hypercenterC22×#41D269
hypocenterC269C2×#413
LCSG ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8608

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, 12985);