Finite Group Databasebeta

C2×#31770485 #46813304

order34432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#31770485

Splittings

SylowC269 ⋊ C2×#386

Subgroups

subgroupG/H
centerC24C22×D269
commutatorC22×C269C23×C4
FrattiniC23C23×D269
Fitting, prime radicalC23×D4×C269C2
socleC24×C269C23
cosocleC23×C269C24
hypercenterC23×D4D269
hypocenterC269C2×#386
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C24 ◁ C23×D4

1576 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, 6929);