Finite Group DatabasebetaFinite Group Databasebeta| order | 12480 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8257536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C43 |
| abelian | C3×C43×C5×C13 |
| multiplicative | (ℤ/16165)ˣ, (ℤ/17225)ˣ, (ℤ/32330)ˣ, (ℤ/34450)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23 | C23×C3×C5×C13 |
| socle, prime radical | C23×C3×C5×C13 | C23 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1032 conjugacy classes of subgroups.
12480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C42×C5×C8×C13, C2×C3×C43×C5×C13 |
| maximal normal subgroup of | C3×C42×C5×C8×C13, C2×C3×C43×C5×C13 |
| maximal quotient of | C3×C42×C5×C8×C13, C2×C3×C43×C5×C13 |
Past the SmallGroups library coverage — no SmallGroups id.