Finite Group DatabasebetaFinite Group Databasebeta| order | 7128 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 970444800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C36 |
| abelian | C34×C8×C11 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C2×C34×C11 |
| socle, prime radical | C2×C34×C11 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1696 conjugacy classes of subgroups.
7128 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C34×C11×C16, C2×C34×C8×C11, C33×C8×C9×C11, … |
| maximal normal subgroup of | C34×C11×C16, C2×C34×C8×C11, C33×C8×C9×C11, … |
| maximal quotient of | C34×C11×C16, C2×C34×C8×C11, C33×C8×C9×C11, … |
Past the SmallGroups library coverage — no SmallGroups id.