Finite Group DatabasebetaFinite Group Databasebeta| order | 6664 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 129024 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C7 |
| abelian | C72×C8×C17 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C2×C72×C17 |
| socle, prime radical | C2×C72×C17 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
80 conjugacy classes of subgroups.
6664 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×C16×C17, C2×C72×C8×C17, C3×C72×C8×C17 |
| maximal normal subgroup of | C72×C16×C17, C2×C72×C8×C17, C3×C72×C8×C17 |
| maximal quotient of | C72×C16×C17, C2×C72×C8×C17, C3×C72×C8×C17 |
Past the SmallGroups library coverage — no SmallGroups id.