Finite Group Databasebeta

C2×#31771136 #46824148

order34432
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#31771136

Splittings

SylowC269 ⋊ C2×#529

Subgroups

subgroupG/H
centerC23C23×D269
commutator, cosocleC22×C269C25
FrattiniC22C24×D269
Fitting, prime radicalC2×#121×C269C2
socleC23×C269C24
hypercenterC2×#121D269
hypocenterC269C2×#529
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ C2×#121

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

3808 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 17773);