Finite Group Databasebeta

C2×#31770369 #46810608

order34432
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#31770369

Splittings

SylowC269 ⋊ C2×#341

Subgroups

subgroupG/H
centerC22×C4C22⋊D269
commutatorC4×C269C2×C42
FrattiniC22×C4C22×D269
FittingC22×M16×C269C2
socleC23×C269C4⋊C4
prime radicalC24×C269Q8
cosocleC22×C4×C269C23
hypercenterC22×M16D269
hypocenterC269C2×#341
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

392 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, 4233);