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Elements of the group are displayed as permutations of degree 18.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 7P | ||||||
| $\SOPlus(4,8)$ | 1A | $1$ | $1$ | $\SOPlus(4,8)$ | 1A | 1A | 1A | $()$ |
| $\SOPlus(4,8)$ | 2A | $2$ | $126$ | $C_2^3\times \SL(2,8)$ | 1A | 2A | 2A | $(1,4)(2,8)(5,6)(7,9)$ |
| $\SOPlus(4,8)$ | 2B | $2$ | $504$ | $C_2\times \SL(2,8)$ | 1A | 2B | 2B | $(1,16)(2,11)(3,18)(4,15)(5,17)(6,13)(7,10)(8,14)(9,12)$ |
| $\SOPlus(4,8)$ | 2C | $2$ | $3969$ | $C_2^3\wr C_2$ | 1A | 2C | 2C | $(1,9)(2,3)(4,5)(6,7)(10,12)(11,17)(13,16)(15,18)$ |
| $\SOPlus(4,8)$ | 3A | $3$ | $112$ | $C_9\times \SL(2,8)$ | 3A | 1A | 3A | $(1,9,3)(2,7,8)(4,6,5)$ |
| $\SOPlus(4,8)$ | 3B | $3$ | $3136$ | $C_9\times D_9$ | 3B | 1A | 3B | $(1,3,4)(2,5,7)(6,8,9)(10,11,17)(12,13,14)(15,16,18)$ |
| $\SOPlus(4,8)$ | 4A | $4$ | $31752$ | $C_2^2\times C_4$ | 2C | 4A | 4A | $(1,15,9,18)(2,13,3,16)(4,11,5,17)(6,10,7,12)(8,14)$ |
| $\SOPlus(4,8)$ | 6A | $6$ | $7056$ | $C_2^2\times C_{18}$ | 3A | 2A | 6A | $(1,6,2)(3,9,4)(5,8,7)(10,11)(13,17)(14,16)(15,18)$ |
| $\SOPlus(4,8)$ | 6B | $6$ | $28224$ | $C_{18}$ | 3B | 2B | 6B | $(1,15,3,16,4,18)(2,10,5,11,7,17)(6,12,8,13,9,14)$ |
| $\SOPlus(4,8)$ | 7A1 | $7$ | $144$ | $\GL(2,8)$ | 7A2 | 7A3 | 1A | $(12,15,16,17,13,14,18)$ |
| $\SOPlus(4,8)$ | 7A2 | $7$ | $144$ | $\GL(2,8)$ | 7A3 | 7A1 | 1A | $(12,16,13,18,15,17,14)$ |
| $\SOPlus(4,8)$ | 7A3 | $7$ | $144$ | $\GL(2,8)$ | 7A1 | 7A2 | 1A | $(12,17,18,16,14,15,13)$ |
| $\SOPlus(4,8)$ | 7B1 | $7$ | $5184$ | $C_7\times D_7$ | 7B2 | 7B3 | 1A | $(1,7,8,6,9,3,2)(10,15,16,12,14,18,11)$ |
| $\SOPlus(4,8)$ | 7B2 | $7$ | $5184$ | $C_7\times D_7$ | 7B3 | 7B1 | 1A | $(1,8,9,2,7,6,3)(10,16,14,11,15,12,18)$ |
| $\SOPlus(4,8)$ | 7B3 | $7$ | $5184$ | $C_7\times D_7$ | 7B1 | 7B2 | 1A | $(1,6,2,8,3,7,9)(10,12,11,16,18,15,14)$ |
| $\SOPlus(4,8)$ | 7C1 | $7$ | $10368$ | $C_7^2$ | 7C2 | 7C3 | 1A | $(1,9,7,3,8,2,6)(10,14,16,18,11,15,17)$ |
| $\SOPlus(4,8)$ | 7C2 | $7$ | $10368$ | $C_7^2$ | 7C3 | 7C1 | 1A | $(1,7,8,6,9,3,2)(10,16,11,17,14,18,15)$ |
| $\SOPlus(4,8)$ | 7C3 | $7$ | $10368$ | $C_7^2$ | 7C1 | 7C2 | 1A | $(1,3,6,7,2,9,8)(10,18,17,16,15,14,11)$ |
| $\SOPlus(4,8)$ | 9A1 | $9$ | $112$ | $C_9\times \SL(2,8)$ | 9A2 | 3A | 9A2 | $(1,6,2,9,5,7,3,4,8)$ |
| $\SOPlus(4,8)$ | 9A2 | $9$ | $112$ | $C_9\times \SL(2,8)$ | 9A4 | 3A | 9A4 | $(1,2,5,3,8,6,9,7,4)$ |
| $\SOPlus(4,8)$ | 9A4 | $9$ | $112$ | $C_9\times \SL(2,8)$ | 9A1 | 3A | 9A1 | $(1,5,8,9,4,2,3,6,7)$ |
| $\SOPlus(4,8)$ | 9B1 | $9$ | $3136$ | $C_9\times D_9$ | 9B2 | 3B | 9B2 | $(1,9,5,3,6,7,4,8,2)(10,15,14,11,16,12,17,18,13)$ |
| $\SOPlus(4,8)$ | 9B2 | $9$ | $3136$ | $C_9\times D_9$ | 9B4 | 3B | 9B4 | $(1,5,6,4,2,9,3,7,8)(10,14,16,17,13,15,11,12,18)$ |
| $\SOPlus(4,8)$ | 9B4 | $9$ | $3136$ | $C_9\times D_9$ | 9B1 | 3B | 9B1 | $(1,6,2,3,8,5,4,9,7)(10,16,13,11,18,14,17,15,12)$ |
| $\SOPlus(4,8)$ | 9C1 | $9$ | $6272$ | $C_9^2$ | 9C2 | 3B | 9C2 | $(1,7,3,4,9,6,5,8,2)(10,13,14,15,17,18,12,11,16)$ |
| $\SOPlus(4,8)$ | 9C2 | $9$ | $6272$ | $C_9^2$ | 9C4 | 3B | 9C4 | $(1,3,9,5,2,7,4,6,8)(10,14,17,12,16,13,15,18,11)$ |
| $\SOPlus(4,8)$ | 9C4 | $9$ | $6272$ | $C_9^2$ | 9C1 | 3B | 9C1 | $(1,9,2,4,8,3,5,7,6)(10,17,16,15,11,14,12,13,18)$ |
| $\SOPlus(4,8)$ | 9D1 | $9$ | $6272$ | $C_9^2$ | 9D2 | 3A | 9D2 | $(1,3,7,2,4,8,6,9,5)(10,12,14)(11,18,13)(15,17,16)$ |
| $\SOPlus(4,8)$ | 9D2 | $9$ | $6272$ | $C_9^2$ | 9D4 | 3A | 9D4 | $(1,7,4,6,5,3,2,8,9)(10,14,12)(11,13,18)(15,16,17)$ |
| $\SOPlus(4,8)$ | 9D4 | $9$ | $6272$ | $C_9^2$ | 9D1 | 3A | 9D1 | $(1,4,5,2,9,7,6,3,8)(10,12,14)(11,18,13)(15,17,16)$ |
| $\SOPlus(4,8)$ | 14A1 | $14$ | $9072$ | $C_2^2\times C_{14}$ | 7A1 | 14A3 | 2A | $(1,4)(2,8)(5,6)(7,9)(12,13,15,14,16,18,17)$ |
| $\SOPlus(4,8)$ | 14A3 | $14$ | $9072$ | $C_2^2\times C_{14}$ | 7A3 | 14A5 | 2A | $(1,4)(2,8)(5,6)(7,9)(12,14,17,15,18,13,16)$ |
| $\SOPlus(4,8)$ | 14A5 | $14$ | $9072$ | $C_2^2\times C_{14}$ | 7A2 | 14A1 | 2A | $(1,4)(2,8)(5,6)(7,9)(12,18,14,13,17,16,15)$ |
| $\SOPlus(4,8)$ | 14B1 | $14$ | $36288$ | $C_{14}$ | 7B1 | 14B3 | 2B | $(1,11,7,10,8,15,6,16,9,12,3,14,2,18)(4,17)(5,13)$ |
| $\SOPlus(4,8)$ | 14B3 | $14$ | $36288$ | $C_{14}$ | 7B3 | 14B5 | 2B | $(1,10,6,12,2,11,8,16,3,18,7,15,9,14)(4,17)(5,13)$ |
| $\SOPlus(4,8)$ | 14B5 | $14$ | $36288$ | $C_{14}$ | 7B2 | 14B1 | 2B | $(1,15,3,11,6,14,7,16,2,10,9,18,8,12)(4,17)(5,13)$ |
| $\SOPlus(4,8)$ | 18A1 | $18$ | $7056$ | $C_2^2\times C_{18}$ | 9A2 | 6A | 18A7 | $(1,7,4,6,5,3,2,8,9)(10,11)(13,17)(14,16)(15,18)$ |
| $\SOPlus(4,8)$ | 18A5 | $18$ | $7056$ | $C_2^2\times C_{18}$ | 9A1 | 6A | 18A1 | $(1,3,7,2,4,8,6,9,5)(10,11)(13,17)(14,16)(15,18)$ |
| $\SOPlus(4,8)$ | 18A7 | $18$ | $7056$ | $C_2^2\times C_{18}$ | 9A4 | 6A | 18A5 | $(1,8,3,6,7,9,2,5,4)(10,11)(13,17)(14,16)(15,18)$ |
| $\SOPlus(4,8)$ | 18B1 | $18$ | $28224$ | $C_{18}$ | 9B1 | 6B | 18B7 | $(1,10,9,15,5,14,3,11,6,16,7,12,4,17,8,18,2,13)$ |
| $\SOPlus(4,8)$ | 18B5 | $18$ | $28224$ | $C_{18}$ | 9B4 | 6B | 18B1 | $(1,14,7,18,9,11,4,13,5,16,8,10,3,12,2,15,6,17)$ |
| $\SOPlus(4,8)$ | 18B7 | $18$ | $28224$ | $C_{18}$ | 9B2 | 6B | 18B5 | $(1,11,8,15,7,13,3,17,9,16,2,14,4,10,6,18,5,12)$ |
| $\SOPlus(4,8)$ | 21A1 | $21$ | $8064$ | $C_{63}$ | 21A2 | 7A2 | 3A | $(1,9,3)(2,7,8)(4,6,5)(10,13,17,11,16,12,14)$ |
| $\SOPlus(4,8)$ | 21A2 | $21$ | $8064$ | $C_{63}$ | 21A4 | 7A3 | 3A | $(1,3,9)(2,8,7)(4,5,6)(10,17,16,14,13,11,12)$ |
| $\SOPlus(4,8)$ | 21A4 | $21$ | $8064$ | $C_{63}$ | 21A1 | 7A1 | 3A | $(1,9,3)(2,7,8)(4,6,5)(10,16,13,12,17,14,11)$ |
| $\SOPlus(4,8)$ | 63A1 | $63$ | $8064$ | $C_{63}$ | 63A2 | 21A1 | 9A1 | $(1,5,8,9,4,2,3,6,7)(10,12,11,13,14,16,17)$ |
| $\SOPlus(4,8)$ | 63A2 | $63$ | $8064$ | $C_{63}$ | 63A4 | 21A2 | 9A2 | $(1,8,4,3,7,5,9,2,6)(10,11,14,17,12,13,16)$ |
| $\SOPlus(4,8)$ | 63A4 | $63$ | $8064$ | $C_{63}$ | 63A1 | 21A4 | 9A4 | $(1,4,7,9,6,8,3,5,2)(10,14,12,16,11,17,13)$ |
| $\SOPlus(4,8)$ | 63A5 | $63$ | $8064$ | $C_{63}$ | 63A10 | 21A2 | 9A4 | $(1,2,5,3,8,6,9,7,4)(10,16,13,12,17,14,11)$ |
| $\SOPlus(4,8)$ | 63A10 | $63$ | $8064$ | $C_{63}$ | 63A20 | 21A4 | 9A1 | $(1,5,8,9,4,2,3,6,7)(10,13,17,11,16,12,14)$ |