Finite Group Databasebeta

#471×D269 #46820580

order34432
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#471×D269

Splittings

Fitting#471×C269 ⋊ C2
SylowC269 ⋊ C2×#471

Subgroups

subgroupG/H
centerC2#121×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#471×C269C2
socleC2×C269C2×#121
prime radicalAGL(1,ℤ/8)×D269C2
hypercenter#471D269
hypocenterC269C2×#471
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4304

Conjugacy classes & character table

2176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 14205);