Finite Group DatabasebetaFinite Group Databasebeta| order | 11997 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C31×C43 ⋊ C9 |
| Sylow | C43 ⋊ C31⋊C9 |
| Sylow | C31 ⋊ C43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #16860688 |
| commutator, hypocenter | C31×C43 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C31×C43 | C3 |
| LCS | G ▷ C31×C43 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3,31,43,3|a^3=d,b^a=b^25,c^a=c^61341 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#26046341, #37562008, #37562012, … |
| maximal normal subgroup of | C2×#26046341, #37562008, #37562012, … |
| maximal quotient of | C2×#26046341 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11997, 5);