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Elements of the group are displayed as permutations of degree 20.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||
|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 7P | ||||||
| $C_2^{10}.S_{10}$ | 1A | $1$ | $1$ | not computed | 1A | 1A | 1A | 1A | $()$ |
| $C_2^{10}.S_{10}$ | 2A | $2$ | $1$ | not computed | 1A | 2A | 2A | 2A | $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2B | $2$ | $10$ | not computed | 1A | 2B | 2B | 2B | $(19,20)$ |
| $C_2^{10}.S_{10}$ | 2C | $2$ | $10$ | not computed | 1A | 2C | 2C | 2C | $(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2D | $2$ | $45$ | not computed | 1A | 2D | 2D | 2D | $(11,12)(17,18)$ |
| $C_2^{10}.S_{10}$ | 2E | $2$ | $45$ | not computed | 1A | 2E | 2E | 2E | $(1,2)(3,4)(7,8)(9,10)(11,12)(15,16)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2F | $2$ | $90$ | not computed | 1A | 2F | 2F | 2F | $(3,15)(4,16)$ |
| $C_2^{10}.S_{10}$ | 2G | $2$ | $90$ | not computed | 1A | 2G | 2G | 2G | $(1,2)(3,15)(4,16)(5,6)(7,8)(9,10)(11,12)(13,14)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2H | $2$ | $120$ | not computed | 1A | 2H | 2H | 2H | $(9,10)(11,12)(13,14)$ |
| $C_2^{10}.S_{10}$ | 2I | $2$ | $120$ | not computed | 1A | 2I | 2I | 2I | $(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2J | $2$ | $210$ | not computed | 1A | 2J | 2J | 2J | $(5,6)(11,12)(13,14)(17,18)$ |
| $C_2^{10}.S_{10}$ | 2K | $2$ | $210$ | not computed | 1A | 2K | 2K | 2K | $(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2L | $2$ | $252$ | not computed | 1A | 2L | 2L | 2L | $(9,10)(11,12)(13,14)(15,16)(17,18)$ |
| $C_2^{10}.S_{10}$ | 2M | $2$ | $720$ | not computed | 1A | 2M | 2M | 2M | $(11,13)(12,14)(15,16)$ |
| $C_2^{10}.S_{10}$ | 2N | $2$ | $720$ | not computed | 1A | 2N | 2N | 2N | $(3,4)(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2O | $2$ | $2520$ | not computed | 1A | 2O | 2O | 2O | $(9,17)(10,18)(11,19)(12,20)$ |
| $C_2^{10}.S_{10}$ | 2P | $2$ | $2520$ | not computed | 1A | 2P | 2P | 2P | $(7,9)(8,10)(15,16)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2Q | $2$ | $2520$ | not computed | 1A | 2Q | 2Q | 2Q | $(1,2)(7,9)(8,10)(11,12)(13,14)(15,16)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2R | $2$ | $2520$ | not computed | 1A | 2R | 2R | 2R | $(1,2)(3,4)(5,6)(7,15)(8,16)(9,10)(11,12)(13,17)(14,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2S | $2$ | $5040$ | not computed | 1A | 2S | 2S | 2S | $(7,9)(8,10)(11,12)(13,14)(15,16)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2T | $2$ | $5040$ | not computed | 1A | 2T | 2T | 2T | $(5,6)(7,9)(8,10)(15,16)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2U | $2$ | $6300$ | not computed | 1A | 2U | 2U | 2U | $(3,4)(9,10)(11,17)(12,18)(13,14)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2V | $2$ | $15120$ | not computed | 1A | 2V | 2V | 2V | $(5,19)(6,20)(7,9)(8,10)(15,16)$ |
| $C_2^{10}.S_{10}$ | 2W | $2$ | $15120$ | not computed | 1A | 2W | 2W | 2W | $(1,2)(5,19)(6,20)(7,9)(8,10)(11,12)(13,14)(15,16)(17,18)$ |
| $C_2^{10}.S_{10}$ | 2X | $2$ | $25200$ | not computed | 1A | 2X | 2X | 2X | $(5,13)(6,14)(7,9)(8,10)(11,17)(12,18)$ |
| $C_2^{10}.S_{10}$ | 2Y | $2$ | $25200$ | not computed | 1A | 2Y | 2Y | 2Y | $(1,2)(3,4)(5,13)(6,14)(7,9)(8,10)(11,17)(12,18)(15,16)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2Z | $2$ | $30240$ | not computed | 1A | 2Z | 2Z | 2Z | $(1,14)(2,13)(3,17)(4,18)(5,10)(6,9)(7,20)(8,19)(11,15)(12,16)$ |
| $C_2^{10}.S_{10}$ | 2AA | $2$ | $37800$ | not computed | 1A | 2AA | 2AA | 2AA | $(7,8)(9,17)(10,18)(11,19)(12,20)(15,16)$ |
| $C_2^{10}.S_{10}$ | 2AB | $2$ | $37800$ | not computed | 1A | 2AB | 2AB | 2AB | $(3,4)(5,6)(7,9)(8,10)(11,17)(12,18)(13,14)(15,16)$ |
| $C_2^{10}.S_{10}$ | 2AC | $2$ | $50400$ | not computed | 1A | 2AC | 2AC | 2AC | $(7,15)(8,16)(9,10)(11,12)(13,17)(14,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2AD | $2$ | $75600$ | not computed | 1A | 2AD | 2AD | 2AD | $(1,8)(2,7)(3,11)(4,12)(9,15)(10,16)(13,17)(14,18)$ |
| $C_2^{10}.S_{10}$ | 2AE | $2$ | $75600$ | not computed | 1A | 2AE | 2AE | 2AE | $(1,2)(3,6)(4,5)(7,16)(8,15)(9,20)(10,19)(11,12)(13,18)(14,17)$ |
| $C_2^{10}.S_{10}$ | 2AF | $2$ | $100800$ | not computed | 1A | 2AF | 2AF | 2AF | $(3,5)(4,6)(7,15)(8,16)(9,11)(10,12)(13,14)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2AG | $2$ | $100800$ | not computed | 1A | 2AG | 2AG | 2AG | $(1,2)(3,5)(4,6)(7,15)(8,16)(9,11)(10,12)$ |
| $C_2^{10}.S_{10}$ | 2AH | $2$ | $151200$ | not computed | 1A | 2AH | 2AH | 2AH | $(1,18)(2,17)(3,10)(4,9)(7,15)(8,16)(11,12)(19,20)$ |
| $C_2^{10}.S_{10}$ | 2AI | $2$ | $151200$ | not computed | 1A | 2AI | 2AI | 2AI | $(1,2)(3,18)(4,17)(5,13)(6,14)(7,20)(8,19)(9,11)(10,12)$ |
| $C_2^{10}.S_{10}$ | 3A | $3$ | $960$ | not computed | 3A | 1A | 3A | 3A | $(15,19,17)(16,20,18)$ |
| $C_2^{10}.S_{10}$ | 3B | $3$ | $134400$ | not computed | 3B | 1A | 3B | 3B | $(5,11,7)(6,12,8)(9,14,18)(10,13,17)$ |
| $C_2^{10}.S_{10}$ | 3C | $3$ | $1433600$ | not computed | 3C | 1A | 3C | 3C | $(3,6,7)(4,5,8)(9,17,14)(10,18,13)(11,19,16)(12,20,15)$ |
| $C_2^{10}.S_{10}$ | 4A | $4$ | $90$ | not computed | 2D | 4A | 4A | 4A | $(3,16,4,15)$ |
| $C_2^{10}.S_{10}$ | 4B | $4$ | $90$ | not computed | 2D | 4B | 4B | 4B | $(1,2)(3,16,4,15)(5,6)(7,8)(9,10)(11,12)(13,14)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 4C | $4$ | $720$ | not computed | 2D | 4C | 4C | 4C | $(11,18,12,17)(19,20)$ |
| $C_2^{10}.S_{10}$ | 4D | $4$ | $720$ | not computed | 2D | 4D | 4D | 4D | $(1,2)(5,6)(7,8)(9,10)(11,18,12,17)(13,14)(15,16)(19,20)$ |
| $C_2^{10}.S_{10}$ | 4E | $4$ | $2520$ | not computed | 2J | 4E | 4E | 4E | $(9,17,10,18)(11,19,12,20)$ |
| $C_2^{10}.S_{10}$ | 4F | $4$ | $2520$ | not computed | 2D | 4F | 4F | 4F | $(7,10,8,9)(15,16)(19,20)$ |
| $C_2^{10}.S_{10}$ | 4G | $4$ | $2520$ | not computed | 2D | 4G | 4G | 4G | $(5,6)(7,10,8,9)(11,12)(13,14)(15,16)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 4H | $4$ | $2520$ | not computed | 2J | 4H | 4H | 4H | $(1,2)(3,4)(5,6)(7,16,8,15)(9,10)(11,12)(13,18,14,17)(19,20)$ |
| $C_2^{10}.S_{10}$ | 4I | $4$ | $5040$ | not computed | 2D | 4I | 4I | 4I | $(7,10,8,9)(11,12)(13,14)(15,16)(17,18)(19,20)$ |
| $C_2^{10}.S_{10}$ | 4J | $4$ | $5040$ | not computed | 2D | 4J | 4J | 4J | $(5,6)(7,10,8,9)(15,16)(19,20)$ |
| $C_2^{10}.S_{10}$ | 4K | $4$ | $5040$ | not computed | 2D | 4K | 4K | 4K | $(7,16,8,15)(13,17)(14,18)$ |