This group is not stored in the database. However, basic information about the group, computed on the fly, is listed below.
Group information
| Description: | $C_{3490}$ |
| Order: | \(3490\)\(\medspace = 2 \cdot 5 \cdot 349 \) |
| Exponent: | \(3490\)\(\medspace = 2 \cdot 5 \cdot 349 \) |
| Automorphism group: | $C_{4} \times C_{348}$, of order \(1392\)\(\medspace = 2^{4} \cdot 3 \cdot 29 \) |
| Outer automorphisms: | Group of order \(1392\)\(\medspace = 2^{4} \cdot 3 \cdot 29 \) |
| Nilpotency class: | $1$ |
| Derived length: | $1$ |
This group is cyclic (hence abelian, nilpotent, solvable, supersolvable, monomial, elementary ($p = 2,5,349$), hyperelementary, metacyclic, metabelian, a Z-group, and an A-group). Whether it is metacyclic or rational has not been computed.
Group statistics
| Order | 1 | 2 | 5 | 10 | 349 | 698 | 1745 | 3490 | |
|---|---|---|---|---|---|---|---|---|---|
| Elements | 1 | 1 | 4 | 4 | 348 | 348 | 1392 | 1392 | 3490 |
| Conjugacy classes | 1 | 1 | 4 | 4 | 348 | 348 | 1392 | 1392 | 3490 |
| Divisions | data not computed | ||||||||
| Autjugacy classes | data not computed | ||||||||
| Dimension | 1 | |
|---|---|---|
| Irr. complex chars. | 3490 | 3490 |
Constructions
| Rank: | $1$ |
| Inequivalent generators: | not computed |
Homology
| Primary decomposition: | $C_{2} \times C_{5} \times C_{349}$ |
Subgroups
| Center: | $Z \simeq$ $C_{3490}$ | $G/Z \simeq$ $C_1$ | |
| Commutator: | $G' \simeq$ $C_1$ | $G/G' \simeq$ $C_{3490}$ | |
| Frattini: | $\Phi \simeq$ $C_1$ | $G/\Phi \simeq$ $C_{3490}$ | |
| Fitting: | $\operatorname{Fit} \simeq$ $C_{3490}$ | $G/\operatorname{Fit} \simeq$ $C_1$ | |
| Radical: | $R \simeq$ $C_{3490}$ | $G/R \simeq$ $C_1$ | |
| Socle: | $S \simeq$ $C_{3490}$ | $G/S \simeq$ $C_1$ | |
| 2-Sylow subgroup: | $P_{2} \simeq$ $C_2$ | ||
| 5-Sylow subgroup: | $P_{5} \simeq$ $C_5$ | ||
| 349-Sylow subgroup: | $P_{349} \simeq$ $C_{349}$ |