Finite Group DatabasebetaFinite Group Databasebeta| order | 8541 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C73 ⋊ C9 |
| Sylow | C73 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ #10620323 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C73 | C9 |
| LCS | G ▷ C13×C73 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,13,73|a^3=b,c^a=c^3,d^a=d^2,d^b=d^8125 conjugacy classes — view the full character table.
| maximal subgroup of | #30685165, #30685167, #30685171, … |
| maximal normal subgroup of | #30685165, #30685167, #30685171, … |
| maximal quotient of | C2×#22555439, C22⋊#22555439 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8541, 8);