Finite Group Databasebeta

C2×#31771083 #46824076

order34432
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#31771083

Splittings

SylowC269 ⋊ C2×#519

Subgroups

subgroupG/H
centerC23C23×D269
commutatorC2×C269C24×C4
FrattiniC22C24×D269
FittingC23×Q8×C269C2
socleC23×C269C24
prime radicalC24×C269C23
cosocleC22×C269C25
hypercenterC23×Q8D269
hypocenterC269C2×#519
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C23 ◁ C23×Q8

1488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

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, 17701);