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Elements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\SU(4,7)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 7P | 43P | ||||||
| $\PSU(4,7)$ | 1A | $1$ | $1$ | not computed | 1A | 1A | 1A | 1A | 1A | $ \left[ \left(\begin{array}{rrrr} 0 & -1 & -1 & -1 \\ -1 & 0 & -1 & -1 \\ -1 & -1 & 0 & -1 \\ -1 & -1 & -1 & 0 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 2A | $2$ | $102900$ | not computed | 1A | 2A | 2A | 2A | 2A | $ \left[ \left(\begin{array}{rrrr} -1 & -1 & 19 & 10 \\ 33 & 42 & 34 & 25 \\ -1 & -1 & 42 & -1 \\ 26 & -1 & 27 & -1 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 2B | $2$ | $2581075$ | not computed | 1A | 2B | 2B | 2B | 2B | $ \left[ \left(\begin{array}{rrrr} 26 & 34 & 19 & 36 \\ 24 & 31 & 36 & 13 \\ 35 & 44 & 1 & 22 \\ 4 & 29 & 0 & 14 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 3A | $3$ | $6607552$ | not computed | 3A | 1A | 3A | 3A | 3A | $ \left[ \left(\begin{array}{rrrr} 28 & 16 & 12 & 16 \\ 32 & 28 & 8 & 36 \\ 20 & 8 & 44 & 16 \\ 0 & 44 & 32 & 44 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 3B | $3$ | $289080400$ | not computed | 3B | 1A | 3B | 3B | 3B | $ \left[ \left(\begin{array}{rrrr} 20 & 39 & 44 & 44 \\ 43 & 13 & 44 & 44 \\ 36 & 14 & -1 & 0 \\ 14 & 6 & 24 & 40 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 4A | $4$ | $5162150$ | not computed | 2B | 4A | 4A | 4A | 4A | $ \left[ \left(\begin{array}{rrrr} 3 & 2 & 35 & 4 \\ 40 & 27 & 4 & 29 \\ 3 & 12 & 47 & 38 \\ 20 & 45 & 16 & 28 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 4B | $4$ | $216810300$ | not computed | 2B | 4B | 4B | 4B | 4B | $ \left[ \left(\begin{array}{rrrr} 2 & 23 & 26 & 23 \\ 32 & 24 & 1 & 14 \\ 40 & 13 & 19 & 27 \\ 47 & 33 & 24 & 23 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 4C | $4$ | $2276508150$ | not computed | 2B | 4C | 4C | 4C | 4C | $ \left[ \left(\begin{array}{rrrr} 42 & 33 & 10 & 2 \\ 0 & 40 & 28 & 20 \\ 18 & 16 & 0 & 33 \\ 34 & 41 & 14 & 21 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 5A | $5$ | $15540962304$ | not computed | 5A | 5A | 1A | 5A | 5A | $ \left[ \left(\begin{array}{rrrr} 16 & 7 & 23 & 7 \\ 39 & 41 & 34 & 7 \\ 29 & 28 & 36 & 0 \\ 25 & 20 & 14 & 24 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 6A | $6$ | $289080400$ | not computed | 3B | 2B | 6A | 6A | 6A | $ \left[ \left(\begin{array}{rrrr} 28 & 17 & 44 & 44 \\ 23 & 4 & 44 & 44 \\ 25 & 35 & 38 & 36 \\ 35 & 43 & 26 & 35 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 6B | $6$ | $8094251200$ | not computed | 3A | 2B | 6B | 6B | 6B | $ \left[ \left(\begin{array}{rrrr} 5 & 15 & 41 & 37 \\ 27 & 25 & 15 & 28 \\ 46 & 45 & 4 & 0 \\ 2 & 19 & 42 & 41 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 6C | $6$ | $12141376800$ | not computed | 3B | 2A | 6C | 6C | 6C | $ \left[ \left(\begin{array}{rrrr} 23 & 23 & 0 & 24 \\ 4 & 42 & 21 & 41 \\ 29 & 21 & 2 & 19 \\ 1 & 39 & 29 & 30 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 7A | $7$ | $103200$ | not computed | 7A | 7A | 7A | 1A | 7A | $ \left[ \left(\begin{array}{rrrr} 31 & 29 & 28 & 28 \\ 11 & 25 & 28 & 28 \\ 18 & 36 & 26 & 35 \\ 36 & 6 & 5 & 38 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 7B | $7$ | $2889600$ | not computed | 7B | 7B | 7B | 1A | 7B | $ \left[ \left(\begin{array}{rrrr} 35 & 35 & 23 & -1 \\ 20 & 38 & 36 & 41 \\ 43 & 4 & 31 & 29 \\ 4 & 37 & 20 & 7 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 7C | $7$ | $2889600$ | not computed | 7C | 7C | 7C | 1A | 7C | $ \left[ \left(\begin{array}{rrrr} 47 & 14 & 16 & 12 \\ -1 & 41 & -1 & 40 \\ 16 & 12 & 41 & 26 \\ -1 & 40 & -1 & 47 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 7D | $7$ | $242726400$ | not computed | 7D | 7D | 7D | 1A | 7D | $ \left[ \left(\begin{array}{rrrr} 2 & 0 & 32 & 7 \\ 18 & 2 & 11 & 15 \\ 18 & 27 & 47 & 22 \\ 23 & 13 & 4 & 26 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 7E1 | $7$ | $3398169600$ | not computed | 7E1 | 7E-1 | 7E-1 | 1A | 7E1 | $ \left[ \left(\begin{array}{rrrr} 21 & 40 & 28 & 41 \\ 10 & 38 & 26 & 30 \\ 31 & 40 & 10 & 42 \\ 27 & 13 & 43 & 5 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 7E-1 | $7$ | $3398169600$ | not computed | 7E-1 | 7E1 | 7E1 | 1A | 7E-1 | $ \left[ \left(\begin{array}{rrrr} 47 & 18 & 30 & 11 \\ 25 & 34 & 2 & 16 \\ 7 & 4 & 38 & 4 \\ 9 & 37 & 34 & 15 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 7F1 | $7$ | $3398169600$ | not computed | 7F1 | 7F-1 | 7F-1 | 1A | 7F1 | $ \left[ \left(\begin{array}{rrrr} 27 & 6 & 39 & 12 \\ 16 & 41 & 28 & 9 \\ 22 & 1 & 40 & 13 \\ 3 & 44 & 43 & 8 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 7F-1 | $7$ | $3398169600$ | not computed | 7F-1 | 7F1 | 7F1 | 1A | 7F-1 | $ \left[ \left(\begin{array}{rrrr} 20 & 7 & 27 & 0 \\ 25 & 4 & 16 & 45 \\ 32 & 19 & 11 & 6 \\ 33 & 22 & 28 & 9 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 8A1 | $8$ | $216810300$ | not computed | 4B | 8A1 | 8A-1 | 8A-1 | 8A1 | $ \left[ \left(\begin{array}{rrrr} 18 & 24 & 31 & 40 \\ 8 & 22 & 46 & 19 \\ 17 & 20 & 14 & 11 \\ 16 & 33 & 47 & 32 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 8A-1 | $8$ | $216810300$ | not computed | 4B | 8A-1 | 8A1 | 8A1 | 8A-1 | $ \left[ \left(\begin{array}{rrrr} 20 & 17 & 25 & 28 \\ 29 & 38 & 22 & 13 \\ 27 & 32 & 46 & 12 \\ 4 & 11 & 44 & 18 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 8B1 | $8$ | $216810300$ | not computed | 4B | 8B3 | 8B3 | 8B1 | 8B3 | $ \left[ \left(\begin{array}{rrrr} 31 & 5 & 32 & 18 \\ 16 & 16 & 40 & 29 \\ 25 & 2 & 27 & 17 \\ 40 & 5 & 16 & 6 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 8B3 | $8$ | $216810300$ | not computed | 4B | 8B1 | 8B1 | 8B3 | 8B1 | $ \left[ \left(\begin{array}{rrrr} 6 & 36 & 33 & 9 \\ 40 & 24 & 16 & 41 \\ 5 & 41 & 30 & 0 \\ 16 & 14 & 40 & 2 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 8C | $8$ | $8094251200$ | not computed | 4A | 8C | 8C | 8C | 8C | $ \left[ \left(\begin{array}{rrrr} 37 & 27 & 20 & 22 \\ 44 & 14 & 2 & -1 \\ -1 & 23 & 19 & 18 \\ 9 & 4 & 9 & 2 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 8D | $8$ | $9106032600$ | not computed | 4B | 8D | 8D | 8D | 8D | $ \left[ \left(\begin{array}{rrrr} 0 & 40 & 14 & 16 \\ 9 & 2 & 43 & 24 \\ 24 & 18 & 5 & 42 \\ 40 & 33 & 3 & 37 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 8E | $8$ | $9106032600$ | not computed | 4B | 8E | 8E | 8E | 8E | $ \left[ \left(\begin{array}{rrrr} 41 & 39 & 38 & 0 \\ 36 & 6 & 45 & 3 \\ 32 & 9 & 44 & 22 \\ 37 & 12 & 46 & 37 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 12A1 | $12$ | $289080400$ | not computed | 6A | 4A | 12A1 | 12A-1 | 12A-1 | $ \left[ \left(\begin{array}{rrrr} 15 & 26 & 26 & 26 \\ 12 & 34 & 26 & 26 \\ 43 & 36 & 32 & 47 \\ 36 & 13 & 17 & 24 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 12A-1 | $12$ | $289080400$ | not computed | 6A | 4A | 12A-1 | 12A1 | 12A1 | $ \left[ \left(\begin{array}{rrrr} 36 & 5 & 2 & 2 \\ 35 & 44 & 2 & 2 \\ 7 & 24 & 10 & 2 \\ 24 & 25 & 0 & 21 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 12B | $12$ | $12141376800$ | not computed | 6A | 4B | 12B | 12B | 12B | $ \left[ \left(\begin{array}{rrrr} 41 & 0 & 19 & 24 \\ 41 & 4 & 27 & 4 \\ 35 & 42 & 6 & 47 \\ 23 & 34 & 43 & 45 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 12C | $12$ | $16188502400$ | not computed | 6B | 4A | 12C | 12C | 12C | $ \left[ \left(\begin{array}{rrrr} 33 & 33 & 33 & 9 \\ 3 & 46 & 3 & 22 \\ 1 & 13 & 4 & 10 \\ 16 & 11 & 43 & 45 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 14A | $14$ | $212385600$ | not computed | 7A | 14A | 14A | 2A | 14A | $ \left[ \left(\begin{array}{rrrr} 44 & 5 & 23 & 25 \\ 35 & 44 & 35 & 3 \\ 14 & 3 & 19 & 37 \\ 28 & 39 & 33 & 1 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 14B | $14$ | $247783200$ | not computed | 7A | 14B | 14B | 2B | 14B | $ \left[ \left(\begin{array}{rrrr} 44 & 12 & 44 & 31 \\ 38 & 6 & 1 & 12 \\ 28 & 10 & 12 & 18 \\ 9 & 16 & 23 & 39 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 14C | $14$ | $2973398400$ | not computed | 7C | 14C | 14C | 2B | 14C | $ \left[ \left(\begin{array}{rrrr} 16 & 35 & 4 & 23 \\ 13 & 8 & 1 & 44 \\ 29 & 23 & 4 & 23 \\ 46 & 40 & 14 & 30 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 14D | $14$ | $2973398400$ | not computed | 7B | 14D | 14D | 2B | 14D | $ \left[ \left(\begin{array}{rrrr} 46 & 15 & 10 & 9 \\ 32 & 8 & 11 & 33 \\ 26 & 39 & 7 & 1 \\ 11 & 5 & 38 & 3 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 14E | $14$ | $11893593600$ | not computed | 7D | 14E | 14E | 2A | 14E | $ \left[ \left(\begin{array}{rrrr} -1 & 3 & 15 & 34 \\ 21 & 20 & 20 & 2 \\ 1 & 36 & 11 & 30 \\ 2 & 0 & 12 & 30 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 15A1 | $15$ | $15540962304$ | not computed | 15A1 | 5A | 3A | 15A-1 | 15A-1 | $ \left[ \left(\begin{array}{rrrr} 41 & 39 & 34 & 24 \\ 31 & 2 & 7 & 2 \\ 25 & 37 & 12 & 18 \\ 20 & 42 & 21 & 7 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 15A-1 | $15$ | $15540962304$ | not computed | 15A-1 | 5A | 3A | 15A1 | 15A1 | $ \left[ \left(\begin{array}{rrrr} 1 & 30 & 14 & 24 \\ 3 & 36 & 1 & 46 \\ 6 & 19 & 14 & 33 \\ 44 & 31 & 25 & 47 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 16A1 | $16$ | $12141376800$ | not computed | 8A1 | 16A3 | 16A-3 | 16A-1 | 16A3 | $ \left[ \left(\begin{array}{rrrr} 36 & 33 & 7 & 39 \\ 11 & 21 & 30 & 11 \\ 47 & 13 & 29 & 21 \\ 24 & 44 & 16 & 4 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 16A-1 | $16$ | $12141376800$ | not computed | 8A-1 | 16A-3 | 16A3 | 16A1 | 16A-3 | $ \left[ \left(\begin{array}{rrrr} 40 & 15 & 41 & 45 \\ 28 & 23 & 30 & 13 \\ 32 & 7 & 15 & 3 \\ 36 & 5 & 41 & 24 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 16A3 | $16$ | $12141376800$ | not computed | 8A1 | 16A1 | 16A-1 | 16A-3 | 16A1 | $ \left[ \left(\begin{array}{rrrr} 0 & -1 & 20 & 44 \\ 40 & -1 & -1 & 36 \\ 8 & 36 & 28 & 21 \\ 24 & 4 & -1 & 20 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 16A-3 | $16$ | $12141376800$ | not computed | 8A-1 | 16A-1 | 16A1 | 16A3 | 16A-1 | $ \left[ \left(\begin{array}{rrrr} 8 & 15 & 24 & 32 \\ -1 & 16 & -1 & 8 \\ 40 & 24 & -1 & -1 \\ 36 & 20 & 4 & 12 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 21A | $21$ | $7929062400$ | not computed | 21A | 7B | 21A | 3A | 21A | $ \left[ \left(\begin{array}{rrrr} 7 & 42 & 3 & 38 \\ 6 & 17 & 28 & 3 \\ 4 & 0 & 5 & 11 \\ 9 & 35 & 9 & 32 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 21B | $21$ | $7929062400$ | not computed | 21B | 7C | 21B | 3A | 21B | $ \left[ \left(\begin{array}{rrrr} 27 & 13 & 16 & 43 \\ -1 & 29 & -1 & 24 \\ 16 & 32 & 45 & 41 \\ -1 & 24 & -1 & 11 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 21C | $21$ | $13875859200$ | not computed | 21C | 7A | 21C | 3B | 21C | $ \left[ \left(\begin{array}{rrrr} 20 & 28 & 2 & 34 \\ 27 & 6 & 10 & 7 \\ 29 & 15 & 39 & 8 \\ 21 & 7 & 23 & 20 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 24A1 | $24$ | $12141376800$ | not computed | 12B | 8A1 | 24A-1 | 24A-1 | 24A1 | $ \left[ \left(\begin{array}{rrrr} 34 & 40 & 39 & 9 \\ 33 & 21 & 40 & 47 \\ 45 & 38 & 2 & 25 \\ 38 & 31 & 45 & 20 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 24A-1 | $24$ | $12141376800$ | not computed | 12B | 8A-1 | 24A1 | 24A1 | 24A-1 | $ \left[ \left(\begin{array}{rrrr} 32 & 19 & 29 & 3 \\ 15 & 2 & 28 & 21 \\ 13 & 14 & 39 & 28 \\ 14 & 15 & 27 & 34 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 24B1 | $24$ | $12141376800$ | not computed | 12B | 8B1 | 24B5 | 24B1 | 24B5 | $ \left[ \left(\begin{array}{rrrr} 45 & 14 & 22 & 44 \\ 16 & 44 & 40 & 28 \\ 7 & 28 & 10 & 18 \\ 40 & 36 & 16 & 12 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 24B5 | $24$ | $12141376800$ | not computed | 12B | 8B3 | 24B1 | 24B5 | 24B1 | $ \left[ \left(\begin{array}{rrrr} 5 & 10 & 35 & 24 \\ 28 & 45 & 4 & 41 \\ 38 & 8 & 7 & 38 \\ 4 & 17 & 28 & 47 \end{array}\right) \right] $ |
| $\PSU(4,7)$ | 24C1 | $24$ | $16188502400$ | not computed | 12C | 8C | 24C5 | 24C1 | 24C5 | $ \left[ \left(\begin{array}{rrrr} 33 & 31 & 2 & 17 \\ 14 & 9 & 33 & 36 \\ 6 & 8 & -1 & 42 \\ 41 & 47 & 46 & 16 \end{array}\right) \right] $ |