Finite Group DatabasebetaFinite Group Databasebeta| order | 9604 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 406594944 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C73 |
| abelian | C4×C72×C49 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C7 | C2×C73 |
| socle, prime radical | C2×C73 | C2×C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
666 conjugacy classes of subgroups.
9604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×C8×C49, C2×C4×C72×C49, C3×C4×C72×C49 |
| maximal normal subgroup of | C72×C8×C49, C2×C4×C72×C49, C3×C4×C72×C49 |
| maximal quotient of | C72×C8×C49, C2×C4×C72×C49, C3×C4×C72×C49 |
Past the SmallGroups library coverage — no SmallGroups id.