Finite Group Databasebeta

#413×D269 #46819356

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

Aliases

direct product#413×D269

Splittings

Fitting#413×C269 ⋊ C2
SylowC269 ⋊ C2×#413

Subgroups

subgroupG/H
centerC4C22⋊C4×D269
commutatorC22×C269C23×C4
FrattiniC2×C4C23×D269
Fitting#413×C269C2
socleC2×C269C22×C22⋊C4
prime radicalC2×#41×D269C2
cosocleC2×C4×C269C24
hypercenter#413D269
hypocenterC269C2×#413
LCSG ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4304

Conjugacy classes & character table

2992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 12981);