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Elements of the group are displayed as words in the presentation $\langle a \mid a^{996}=1 \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 83P | ||||||
| $C_{996}$ | 1A | $1$ | $1$ | $C_{996}$ | 1A | 1A | 1A | $1$ |
| $C_{996}$ | 2A | $2$ | $1$ | $C_{996}$ | 1A | 2A | 2A | $a^{498}$ |
| $C_{996}$ | 3A1 | $3$ | $1$ | $C_{996}$ | 3A-1 | 1A | 3A-1 | $a^{332}$ |
| $C_{996}$ | 3A-1 | $3$ | $1$ | $C_{996}$ | 3A1 | 1A | 3A1 | $a^{664}$ |
| $C_{996}$ | 4A1 | $4$ | $1$ | $C_{996}$ | 2A | 4A-1 | 4A1 | $a^{249}$ |
| $C_{996}$ | 4A-1 | $4$ | $1$ | $C_{996}$ | 2A | 4A1 | 4A-1 | $a^{747}$ |
| $C_{996}$ | 6A1 | $6$ | $1$ | $C_{996}$ | 3A1 | 2A | 6A-1 | $a^{166}$ |
| $C_{996}$ | 6A-1 | $6$ | $1$ | $C_{996}$ | 3A-1 | 2A | 6A1 | $a^{830}$ |
| $C_{996}$ | 12A1 | $12$ | $1$ | $C_{996}$ | 6A1 | 4A1 | 12A5 | $a^{83}$ |
| $C_{996}$ | 12A-1 | $12$ | $1$ | $C_{996}$ | 6A-1 | 4A-1 | 12A-5 | $a^{913}$ |
| $C_{996}$ | 12A5 | $12$ | $1$ | $C_{996}$ | 6A-1 | 4A1 | 12A1 | $a^{415}$ |
| $C_{996}$ | 12A-5 | $12$ | $1$ | $C_{996}$ | 6A1 | 4A-1 | 12A-1 | $a^{581}$ |
| $C_{996}$ | 83A1 | $83$ | $1$ | $C_{996}$ | 83A2 | 83A3 | 83A41 | $a^{12}$ |
| $C_{996}$ | 83A-1 | $83$ | $1$ | $C_{996}$ | 83A-2 | 83A-3 | 83A-41 | $a^{984}$ |
| $C_{996}$ | 83A2 | $83$ | $1$ | $C_{996}$ | 83A4 | 83A6 | 83A-1 | $a^{24}$ |
| $C_{996}$ | 83A-2 | $83$ | $1$ | $C_{996}$ | 83A-4 | 83A-6 | 83A1 | $a^{972}$ |
| $C_{996}$ | 83A3 | $83$ | $1$ | $C_{996}$ | 83A6 | 83A9 | 83A40 | $a^{36}$ |
| $C_{996}$ | 83A-3 | $83$ | $1$ | $C_{996}$ | 83A-6 | 83A-9 | 83A-40 | $a^{960}$ |
| $C_{996}$ | 83A4 | $83$ | $1$ | $C_{996}$ | 83A8 | 83A12 | 83A-2 | $a^{48}$ |
| $C_{996}$ | 83A-4 | $83$ | $1$ | $C_{996}$ | 83A-8 | 83A-12 | 83A2 | $a^{948}$ |
| $C_{996}$ | 83A5 | $83$ | $1$ | $C_{996}$ | 83A10 | 83A15 | 83A39 | $a^{60}$ |
| $C_{996}$ | 83A-5 | $83$ | $1$ | $C_{996}$ | 83A-10 | 83A-15 | 83A-39 | $a^{936}$ |
| $C_{996}$ | 83A6 | $83$ | $1$ | $C_{996}$ | 83A12 | 83A18 | 83A-3 | $a^{72}$ |
| $C_{996}$ | 83A-6 | $83$ | $1$ | $C_{996}$ | 83A-12 | 83A-18 | 83A3 | $a^{924}$ |
| $C_{996}$ | 83A7 | $83$ | $1$ | $C_{996}$ | 83A14 | 83A21 | 83A38 | $a^{84}$ |
| $C_{996}$ | 83A-7 | $83$ | $1$ | $C_{996}$ | 83A-14 | 83A-21 | 83A-38 | $a^{912}$ |
| $C_{996}$ | 83A8 | $83$ | $1$ | $C_{996}$ | 83A16 | 83A24 | 83A-4 | $a^{96}$ |
| $C_{996}$ | 83A-8 | $83$ | $1$ | $C_{996}$ | 83A-16 | 83A-24 | 83A4 | $a^{900}$ |
| $C_{996}$ | 83A9 | $83$ | $1$ | $C_{996}$ | 83A18 | 83A27 | 83A37 | $a^{108}$ |
| $C_{996}$ | 83A-9 | $83$ | $1$ | $C_{996}$ | 83A-18 | 83A-27 | 83A-37 | $a^{888}$ |
| $C_{996}$ | 83A10 | $83$ | $1$ | $C_{996}$ | 83A20 | 83A30 | 83A-5 | $a^{120}$ |
| $C_{996}$ | 83A-10 | $83$ | $1$ | $C_{996}$ | 83A-20 | 83A-30 | 83A5 | $a^{876}$ |
| $C_{996}$ | 83A11 | $83$ | $1$ | $C_{996}$ | 83A22 | 83A33 | 83A36 | $a^{132}$ |
| $C_{996}$ | 83A-11 | $83$ | $1$ | $C_{996}$ | 83A-22 | 83A-33 | 83A-36 | $a^{864}$ |
| $C_{996}$ | 83A12 | $83$ | $1$ | $C_{996}$ | 83A24 | 83A36 | 83A-6 | $a^{144}$ |
| $C_{996}$ | 83A-12 | $83$ | $1$ | $C_{996}$ | 83A-24 | 83A-36 | 83A6 | $a^{852}$ |
| $C_{996}$ | 83A13 | $83$ | $1$ | $C_{996}$ | 83A26 | 83A39 | 83A35 | $a^{156}$ |
| $C_{996}$ | 83A-13 | $83$ | $1$ | $C_{996}$ | 83A-26 | 83A-39 | 83A-35 | $a^{840}$ |
| $C_{996}$ | 83A14 | $83$ | $1$ | $C_{996}$ | 83A28 | 83A-41 | 83A-7 | $a^{168}$ |
| $C_{996}$ | 83A-14 | $83$ | $1$ | $C_{996}$ | 83A-28 | 83A41 | 83A7 | $a^{828}$ |
| $C_{996}$ | 83A15 | $83$ | $1$ | $C_{996}$ | 83A30 | 83A-38 | 83A34 | $a^{180}$ |
| $C_{996}$ | 83A-15 | $83$ | $1$ | $C_{996}$ | 83A-30 | 83A38 | 83A-34 | $a^{816}$ |
| $C_{996}$ | 83A16 | $83$ | $1$ | $C_{996}$ | 83A32 | 83A-35 | 83A-8 | $a^{192}$ |
| $C_{996}$ | 83A-16 | $83$ | $1$ | $C_{996}$ | 83A-32 | 83A35 | 83A8 | $a^{804}$ |
| $C_{996}$ | 83A17 | $83$ | $1$ | $C_{996}$ | 83A34 | 83A-32 | 83A33 | $a^{204}$ |
| $C_{996}$ | 83A-17 | $83$ | $1$ | $C_{996}$ | 83A-34 | 83A32 | 83A-33 | $a^{792}$ |
| $C_{996}$ | 83A18 | $83$ | $1$ | $C_{996}$ | 83A36 | 83A-29 | 83A-9 | $a^{216}$ |
| $C_{996}$ | 83A-18 | $83$ | $1$ | $C_{996}$ | 83A-36 | 83A29 | 83A9 | $a^{780}$ |
| $C_{996}$ | 83A19 | $83$ | $1$ | $C_{996}$ | 83A38 | 83A-26 | 83A32 | $a^{228}$ |
| $C_{996}$ | 83A-19 | $83$ | $1$ | $C_{996}$ | 83A-38 | 83A26 | 83A-32 | $a^{768}$ |