Finite Group Databasebeta

#416×D269 #46819377

order34432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#416×D269

Splittings

Fitting#416×C269 ⋊ C2
SylowC269 ⋊ C2×#416

Subgroups

subgroupG/H
centerC2×C4D4×D269
commutatorC4×C269C23×C4
FrattiniC2×C4C23×D269
Fitting#416×C269C2
socleC22×C269C22×D4
prime radicalC2×#41×D269C2
cosocleC2×C4×C269C24
hypercenter#416D269
hypocenterC269C2×#416
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8608

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, 13002);