Finite Group Databasebeta

C32×D13×D73 #46802971

order34164
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC32×D13×D73

Splittings

Fitting, socle, HallC32×C13×C73 ⋊ C22
derived, HallC13×C73 ⋊ C22×C32
HallC32×C73 ⋊ C2×D13
HallC32×C13 ⋊ C2×D73
SylowC73 ⋊ C2×C32×D13
SylowC13 ⋊ C2×C32×D73

Subgroups

subgroupG/H
center, hypercenterC32D13×D73
commutator, cosocle, hypocenterC13×C73C22×C32
FrattiniC1G
Fitting, socleC32×C13×C73C22
LCSG ▷ C13×C73
UCSC1 ◁ C32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8541

Conjugacy classes & character table

2736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34164, 337);