Finite Group Databasebeta

C2×#31770736 #46819813

order34432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#31770736

Splittings

SylowC269 ⋊ C2×#446

Subgroups

subgroupG/H
centerC22×C4C22×D269
commutatorC22×C269C23×C4
FrattiniC2×C4C23×D269
FittingC2×C4×Q8×C269C2
socle, prime radicalC23×C269C22×C4
cosocleC2×C4×C269C24
hypercenterC2×C4×Q8D269
hypocenterC269C2×#446
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34432

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, 13438);