Finite Group DatabasebetaFinite Group Databasebeta| order | 12544 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 344064 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C32×C49 |
| multiplicative | (ℤ/25216)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C7×C16 | C23×C7 |
| socle, prime radical | C23×C7 | C2×C7×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
405 conjugacy classes of subgroups.
12544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C4×C49×C64, C2×C8×C32×C49, C42×C32×C49, … |
| maximal normal subgroup of | C2×C4×C49×C64, C2×C8×C32×C49, C42×C32×C49, … |
| maximal quotient of | C2×C4×C49×C64, C2×C8×C32×C49, C42×C32×C49, … |
Past the SmallGroups library coverage — no SmallGroups id.