This group is not stored in the database. However, basic information about the group, computed on the fly, is listed below.
Group information
| Description: | $C_{5076}$ |
| Order: | \(5076\)\(\medspace = 2^{2} \cdot 3^{3} \cdot 47 \) |
| Exponent: | \(5076\)\(\medspace = 2^{2} \cdot 3^{3} \cdot 47 \) |
| Automorphism group: | $C_{2} \times C_{18} \times C_{46}$, of order \(1656\)\(\medspace = 2^{3} \cdot 3^{2} \cdot 23 \) |
| Outer automorphisms: | Group of order \(1656\)\(\medspace = 2^{3} \cdot 3^{2} \cdot 23 \) |
| Nilpotency class: | $1$ |
| Derived length: | $1$ |
This group is cyclic (hence abelian, nilpotent, solvable, supersolvable, monomial, elementary ($p = 2,3,47$), 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 | 3 | 4 | 6 | 9 | 12 | 18 | 27 | 36 | 47 | 54 | 94 | 108 | 141 | 188 | 282 | 423 | 564 | 846 | 1269 | 1692 | 2538 | 5076 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Elements | 1 | 1 | 2 | 2 | 2 | 6 | 4 | 6 | 18 | 12 | 46 | 18 | 46 | 36 | 92 | 92 | 92 | 276 | 184 | 276 | 828 | 552 | 828 | 1656 | 5076 |
| Conjugacy classes | 1 | 1 | 2 | 2 | 2 | 6 | 4 | 6 | 18 | 12 | 46 | 18 | 46 | 36 | 92 | 92 | 92 | 276 | 184 | 276 | 828 | 552 | 828 | 1656 | 5076 |
| Divisions | data not computed | ||||||||||||||||||||||||
| Autjugacy classes | data not computed | ||||||||||||||||||||||||
| Dimension | 1 | |
|---|---|---|
| Irr. complex chars. | 5076 | 5076 |
Constructions
| Rank: | $1$ |
| Inequivalent generators: | not computed |
Homology
| Primary decomposition: | $C_{4} \times C_{27} \times C_{47}$ |
Subgroups
| Center: | $Z \simeq$ $C_{5076}$ | $G/Z \simeq$ $C_1$ | |
| Commutator: | $G' \simeq$ $C_1$ | $G/G' \simeq$ $C_{5076}$ | |
| Frattini: | $\Phi \simeq$ $C_{18}$ | $G/\Phi \simeq$ $C_{282}$ | |
| Fitting: | $\operatorname{Fit} \simeq$ $C_{5076}$ | $G/\operatorname{Fit} \simeq$ $C_1$ | |
| Radical: | $R \simeq$ $C_{5076}$ | $G/R \simeq$ $C_1$ | |
| Socle: | $S \simeq$ $C_{282}$ | $G/S \simeq$ $C_{18}$ | |
| 2-Sylow subgroup: | $P_{2} \simeq$ $C_4$ | ||
| 3-Sylow subgroup: | $P_{3} \simeq$ $C_{27}$ | ||
| 47-Sylow subgroup: | $P_{47} \simeq$ $C_{47}$ |