Finite Group Databasebeta

C3×D13×D101 #30628755

order15756
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D13×D101

Splittings

Fitting, socle, HallC3×C13×C101 ⋊ C22
derived, HallC13×C101 ⋊ C22×C3
HallC3×C101 ⋊ C2×D13
SylowC101 ⋊ C2×C3×D13
HallC3×C13 ⋊ C2×D101
SylowC13 ⋊ C2×C3×D101

Subgroups

subgroupG/H
center, hypercenterC3D13×D101
commutator, cosocle, hypocenterC13×C101C22×C3
FrattiniC1G
Fitting, socleC3×C13×C101C22
LCSG ▷ C13×C101
UCSC1 ◁ C3

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3939

Conjugacy classes & character table

1248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15756, 30);