Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 96768 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C7 |
| abelian | C72×C9×C16 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8 | C2×C3×C72 |
| socle, prime radical | C2×C3×C72 | C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
150 conjugacy classes of subgroups.
7056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×C9×C32, C2×C72×C9×C16, C72×C16×C27, … |
| maximal normal subgroup of | C72×C9×C32, C2×C72×C9×C16, C72×C16×C27, … |
| maximal quotient of | C72×C9×C32, C2×C72×C9×C16, C72×C16×C27, … |
Past the SmallGroups library coverage — no SmallGroups id.