Finite Group Databasebeta

#427×D269 #46819461

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

Aliases

direct product#427×D269

Splittings

Fitting#427×C269 ⋊ C2
SylowC269 ⋊ C2×#427

Subgroups

subgroupG/H
centerC2×C4D4×D269
commutatorC4×C269C23×C4
FrattiniC2×C4C23×D269
Fitting#427×C269C2
socleC22×C269C22×D4
prime radicalC23×D269D4
cosocleC2×C4×C269C24
hypercenter#427D269
hypocenterC269C2×#427
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

512 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, 13086);