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Elements of the group are displayed as words in the presentation $\langle a \mid a^{4648}=1 \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 7P | 83P | ||||||
| $C_{4648}$ | 1A | $1$ | $1$ | $C_{4648}$ | 1A | 1A | 1A | $1$ |
| $C_{4648}$ | 2A | $2$ | $1$ | $C_{4648}$ | 1A | 2A | 2A | $a^{2324}$ |
| $C_{4648}$ | 4A1 | $4$ | $1$ | $C_{4648}$ | 2A | 4A-1 | 4A-1 | $a^{1162}$ |
| $C_{4648}$ | 4A-1 | $4$ | $1$ | $C_{4648}$ | 2A | 4A1 | 4A1 | $a^{3486}$ |
| $C_{4648}$ | 7A1 | $7$ | $1$ | $C_{4648}$ | 7A2 | 7A3 | 1A | $a^{664}$ |
| $C_{4648}$ | 7A-1 | $7$ | $1$ | $C_{4648}$ | 7A-2 | 7A-3 | 1A | $a^{3984}$ |
| $C_{4648}$ | 7A2 | $7$ | $1$ | $C_{4648}$ | 7A-3 | 7A-1 | 1A | $a^{1328}$ |
| $C_{4648}$ | 7A-2 | $7$ | $1$ | $C_{4648}$ | 7A3 | 7A1 | 1A | $a^{3320}$ |
| $C_{4648}$ | 7A3 | $7$ | $1$ | $C_{4648}$ | 7A-1 | 7A2 | 1A | $a^{1992}$ |
| $C_{4648}$ | 7A-3 | $7$ | $1$ | $C_{4648}$ | 7A1 | 7A-2 | 1A | $a^{2656}$ |
| $C_{4648}$ | 8A1 | $8$ | $1$ | $C_{4648}$ | 4A1 | 8A3 | 8A-1 | $a^{581}$ |
| $C_{4648}$ | 8A-1 | $8$ | $1$ | $C_{4648}$ | 4A-1 | 8A-3 | 8A1 | $a^{4067}$ |
| $C_{4648}$ | 8A3 | $8$ | $1$ | $C_{4648}$ | 4A-1 | 8A1 | 8A-3 | $a^{1743}$ |
| $C_{4648}$ | 8A-3 | $8$ | $1$ | $C_{4648}$ | 4A1 | 8A-1 | 8A3 | $a^{2905}$ |
| $C_{4648}$ | 14A1 | $14$ | $1$ | $C_{4648}$ | 7A1 | 14A3 | 2A | $a^{332}$ |
| $C_{4648}$ | 14A-1 | $14$ | $1$ | $C_{4648}$ | 7A-1 | 14A-3 | 2A | $a^{4316}$ |
| $C_{4648}$ | 14A3 | $14$ | $1$ | $C_{4648}$ | 7A3 | 14A-5 | 2A | $a^{996}$ |
| $C_{4648}$ | 14A-3 | $14$ | $1$ | $C_{4648}$ | 7A-3 | 14A5 | 2A | $a^{3652}$ |
| $C_{4648}$ | 14A5 | $14$ | $1$ | $C_{4648}$ | 7A-2 | 14A1 | 2A | $a^{1660}$ |
| $C_{4648}$ | 14A-5 | $14$ | $1$ | $C_{4648}$ | 7A2 | 14A-1 | 2A | $a^{2988}$ |
| $C_{4648}$ | 28A1 | $28$ | $1$ | $C_{4648}$ | 14A1 | 28A3 | 4A1 | $a^{166}$ |
| $C_{4648}$ | 28A-1 | $28$ | $1$ | $C_{4648}$ | 14A-1 | 28A-3 | 4A-1 | $a^{4482}$ |
| $C_{4648}$ | 28A3 | $28$ | $1$ | $C_{4648}$ | 14A3 | 28A9 | 4A-1 | $a^{498}$ |
| $C_{4648}$ | 28A-3 | $28$ | $1$ | $C_{4648}$ | 14A-3 | 28A-9 | 4A1 | $a^{4150}$ |
| $C_{4648}$ | 28A5 | $28$ | $1$ | $C_{4648}$ | 14A5 | 28A-13 | 4A1 | $a^{830}$ |
| $C_{4648}$ | 28A-5 | $28$ | $1$ | $C_{4648}$ | 14A-5 | 28A13 | 4A-1 | $a^{3818}$ |
| $C_{4648}$ | 28A9 | $28$ | $1$ | $C_{4648}$ | 14A-5 | 28A-1 | 4A1 | $a^{1494}$ |
| $C_{4648}$ | 28A-9 | $28$ | $1$ | $C_{4648}$ | 14A5 | 28A1 | 4A-1 | $a^{3154}$ |
| $C_{4648}$ | 28A11 | $28$ | $1$ | $C_{4648}$ | 14A-3 | 28A5 | 4A-1 | $a^{1826}$ |
| $C_{4648}$ | 28A-11 | $28$ | $1$ | $C_{4648}$ | 14A3 | 28A-5 | 4A1 | $a^{2822}$ |
| $C_{4648}$ | 28A13 | $28$ | $1$ | $C_{4648}$ | 14A-1 | 28A11 | 4A1 | $a^{2158}$ |
| $C_{4648}$ | 28A-13 | $28$ | $1$ | $C_{4648}$ | 14A1 | 28A-11 | 4A-1 | $a^{2490}$ |
| $C_{4648}$ | 56A1 | $56$ | $1$ | $C_{4648}$ | 28A1 | 56A3 | 8A1 | $a^{83}$ |
| $C_{4648}$ | 56A-1 | $56$ | $1$ | $C_{4648}$ | 28A-1 | 56A-3 | 8A-1 | $a^{4565}$ |
| $C_{4648}$ | 56A3 | $56$ | $1$ | $C_{4648}$ | 28A3 | 56A9 | 8A3 | $a^{249}$ |
| $C_{4648}$ | 56A-3 | $56$ | $1$ | $C_{4648}$ | 28A-3 | 56A-9 | 8A-3 | $a^{4399}$ |
| $C_{4648}$ | 56A5 | $56$ | $1$ | $C_{4648}$ | 28A5 | 56A15 | 8A-3 | $a^{415}$ |
| $C_{4648}$ | 56A-5 | $56$ | $1$ | $C_{4648}$ | 28A-5 | 56A-15 | 8A3 | $a^{4233}$ |
| $C_{4648}$ | 56A9 | $56$ | $1$ | $C_{4648}$ | 28A9 | 56A27 | 8A1 | $a^{747}$ |
| $C_{4648}$ | 56A-9 | $56$ | $1$ | $C_{4648}$ | 28A-9 | 56A-27 | 8A-1 | $a^{3901}$ |
| $C_{4648}$ | 56A11 | $56$ | $1$ | $C_{4648}$ | 28A11 | 56A-23 | 8A3 | $a^{913}$ |
| $C_{4648}$ | 56A-11 | $56$ | $1$ | $C_{4648}$ | 28A-11 | 56A23 | 8A-3 | $a^{3735}$ |
| $C_{4648}$ | 56A13 | $56$ | $1$ | $C_{4648}$ | 28A13 | 56A-17 | 8A-3 | $a^{1079}$ |
| $C_{4648}$ | 56A-13 | $56$ | $1$ | $C_{4648}$ | 28A-13 | 56A17 | 8A3 | $a^{3569}$ |
| $C_{4648}$ | 56A15 | $56$ | $1$ | $C_{4648}$ | 28A-13 | 56A-11 | 8A-1 | $a^{1245}$ |
| $C_{4648}$ | 56A-15 | $56$ | $1$ | $C_{4648}$ | 28A13 | 56A11 | 8A1 | $a^{3403}$ |
| $C_{4648}$ | 56A17 | $56$ | $1$ | $C_{4648}$ | 28A-11 | 56A-5 | 8A1 | $a^{1411}$ |
| $C_{4648}$ | 56A-17 | $56$ | $1$ | $C_{4648}$ | 28A11 | 56A5 | 8A-1 | $a^{3237}$ |
| $C_{4648}$ | 56A19 | $56$ | $1$ | $C_{4648}$ | 28A-9 | 56A1 | 8A3 | $a^{1577}$ |
| $C_{4648}$ | 56A-19 | $56$ | $1$ | $C_{4648}$ | 28A9 | 56A-1 | 8A-3 | $a^{3071}$ |