Finite Group Databasebeta

C2×#31770632 #46819444

order34432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#31770632

Splittings

SylowC269 ⋊ C2×#424

Subgroups

subgroupG/H
centerC22×C4C22×D269
commutatorC22×C269C23×C4
FrattiniC2×C4C23×D269
FittingC2×#117×C269C2
socleC23×C269C22×C4
prime radicalC24×C269C2×C4
cosocleC2×C4×C269C24
hypercenterC2×#117D269
hypocenterC269C2×#424
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C22×C4 ◁ C2×#117

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

5416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 13069);