Finite Group Databasebeta

#472×D269 #46820588

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

Aliases

direct product#472×D269

Splittings

Fitting#472×C269 ⋊ C2
SylowC269 ⋊ C2×#472

Subgroups

subgroupG/H
centerC2#121×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#472×C269C2
socleC2×C269C2×#121
hypercenter#472D269
hypocenterC269C2×#472
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

488 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, 14213);