Finite Group DatabasebetaFinite Group Databasebeta| order | 12051 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×C103 ⋊ C9 |
| Sylow | C103 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ C103⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #16860816 |
| commutator, hypocenter | C13×C103 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C13×C103 | C3 |
| LCS | G ▷ C13×C103 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3,13,103,3|a^3=d,b^a=b^9,c^a=c^461347 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#27130262, #37562929, #37562933, … |
| maximal normal subgroup of | C2×#27130262, #37562929, #37562933, … |
| maximal quotient of | C2×#27130262 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12051, 5);