Finite Group Databasebeta

#121×Dic269 #46813399

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

Aliases

direct product#121×Dic269

Splittings

SylowC269 ⋊ C4×#121

Subgroups

subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting, prime radicalC2×#121×C269C2
socle, cosocleC23×C269C24
hypercenterC2×#121D269
hypocenterC269C4×#121
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ C2×#121

824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

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, 7024);