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Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{24}=1, b^{a}=b^{11} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_{24}:C_2$ | 1A | $1$ | $1$ | $C_{24}:C_2$ | 1A | 1A | $1$ |
| $C_{24}:C_2$ | 2A | $2$ | $1$ | $C_{24}:C_2$ | 1A | 2A | $b^{12}$ |
| $C_{24}:C_2$ | 2B | $2$ | $12$ | $C_2^2$ | 1A | 2B | $ab^{8}$ |
| $C_{24}:C_2$ | 3A | $3$ | $2$ | $C_{24}$ | 3A | 1A | $b^{8}$ |
| $C_{24}:C_2$ | 4A | $4$ | $2$ | $C_{24}$ | 2A | 4A | $b^{6}$ |
| $C_{24}:C_2$ | 4B | $4$ | $12$ | $C_4$ | 2A | 4B | $ab^{21}$ |
| $C_{24}:C_2$ | 6A | $6$ | $2$ | $C_{24}$ | 3A | 2A | $b^{4}$ |
| $C_{24}:C_2$ | 8A1 | $8$ | $2$ | $C_{24}$ | 4A | 8A1 | $b^{3}$ |
| $C_{24}:C_2$ | 8A-1 | $8$ | $2$ | $C_{24}$ | 4A | 8A-1 | $b^{21}$ |
| $C_{24}:C_2$ | 12A1 | $12$ | $2$ | $C_{24}$ | 6A | 4A | $b^{2}$ |
| $C_{24}:C_2$ | 12A5 | $12$ | $2$ | $C_{24}$ | 6A | 4A | $b^{10}$ |
| $C_{24}:C_2$ | 24A1 | $24$ | $2$ | $C_{24}$ | 12A1 | 8A1 | $b$ |
| $C_{24}:C_2$ | 24A-1 | $24$ | $2$ | $C_{24}$ | 12A1 | 8A-1 | $b^{13}$ |
| $C_{24}:C_2$ | 24A5 | $24$ | $2$ | $C_{24}$ | 12A5 | 8A-1 | $b^{5}$ |
| $C_{24}:C_2$ | 24A-5 | $24$ | $2$ | $C_{24}$ | 12A5 | 8A1 | $b^{17}$ |