Finite Group Databasebeta

C3×D13×D163 #38764008

order25428
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D13×D163

Splittings

Fitting, socle, HallC3×C13×C163 ⋊ C22
derived, HallC13×C163 ⋊ C22×C3
HallC3×C163 ⋊ C2×D13
SylowC163 ⋊ C2×C3×D13
HallC3×C13 ⋊ C2×D163
SylowC13 ⋊ C2×C3×D163

Subgroups

subgroupG/H
center, hypercenterC3D13×D163
commutator, cosocle, hypocenterC13×C163C22×C3
FrattiniC1G
Fitting, socleC3×C13×C163C22
LCSG ▷ C13×C163
UCSC1 ◁ C3

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6357

Conjugacy classes & character table

1992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25428, 52);