Finite Group Databasebeta

C22×#22575364 #46819289

order34432
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productC22×#22575364

Splittings

SylowC269 ⋊ C22×#97

Subgroups

subgroupG/H
centerC23×C4C2×D269
commutatorC2×C269C22×C42
FrattiniC2×C4C23×D269
FittingC22×C42×C269C2
socle, prime radicalC24×C269C2×C4
cosocleC2×C4×C269C24
hypercenterC22×C42D269
hypocenterC269C22×#97
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C23×C4 ◁ C22×C42

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34432

Conjugacy classes & character table

8656 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 12914);