This group is not stored in the database. However, basic information about the group, computed on the fly, is listed below.
Group information
| Description: | $C_{2} \times C_{43740}$ | |
| Order: | \(87480\)\(\medspace = 2^{3} \cdot 3^{7} \cdot 5 \) | |
| Exponent: | \(43740\)\(\medspace = 2^{2} \cdot 3^{7} \cdot 5 \) | |
| Automorphism group: | Group of order 46656 | |
| Nilpotency class: | $1$ | |
| Derived length: | $1$ |
This group is abelian (hence nilpotent, solvable, supersolvable, monomial, metabelian, and an A-group). Whether it is metacyclic or rational has not been computed.
Group statistics
| Order | 1 | 2 | 3 | 4 | 5 | 6 | 9 | 10 | 12 | 15 | 18 | 20 | 27 | 30 | 36 | 45 | 54 | 60 | 81 | 90 | 108 | 135 | 162 | 180 | 243 | 270 | 324 | 405 | 486 | 540 | 729 | 810 | 972 | 1215 | 1458 | 1620 | 2187 | 2430 | 2916 | 3645 | 4374 | 4860 | 7290 | 8748 | 10935 | 14580 | 21870 | 43740 | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Elements | 1 | 3 | 2 | 4 | 4 | 6 | 6 | 12 | 8 | 8 | 18 | 16 | 18 | 24 | 24 | 24 | 54 | 32 | 54 | 72 | 72 | 72 | 162 | 96 | 162 | 216 | 216 | 216 | 486 | 288 | 486 | 648 | 648 | 648 | 1458 | 864 | 1458 | 1944 | 1944 | 1944 | 4374 | 2592 | 5832 | 5832 | 5832 | 7776 | 17496 | 23328 | 87480 | |
| Conjugacy classes | 1 | 3 | 2 | 4 | 4 | 6 | 6 | 12 | 8 | 8 | 18 | 16 | 18 | 24 | 24 | 24 | 54 | 32 | 54 | 72 | 72 | 72 | 162 | 96 | 162 | 216 | 216 | 216 | 486 | 288 | 486 | 648 | 648 | 648 | 1458 | 864 | 1458 | 1944 | 1944 | 1944 | 4374 | 2592 | 5832 | 5832 | 5832 | 7776 | 17496 | 23328 | 87480 | |
| Divisions | data not computed | |||||||||||||||||||||||||||||||||||||||||||||||||
| Autjugacy classes | data not computed | |||||||||||||||||||||||||||||||||||||||||||||||||
| Dimension | 1 | |
|---|---|---|
| Irr. complex chars. | 87480 | 87480 |
Constructions
| Rank: | $2$ |
| Inequivalent generating pairs: | not computed |
Homology
| Primary decomposition: | $C_{2} \times C_{4} \times C_{2187} \times C_{5}$ |
Subgroups
| Center: | $Z \simeq$ $C_{2} \times C_{43740}$ | $G/Z \simeq$ $C_1$ | |
| Commutator: | $G' \simeq$ $C_1$ | $G/G' \simeq$ $C_{2} \times C_{43740}$ | |
| Frattini: | $\Phi \simeq$ $C_{1458}$ | $G/\Phi \simeq$ $C_2\times C_{30}$ | |
| Fitting: | $\operatorname{Fit} \simeq$ $C_{2} \times C_{43740}$ | $G/\operatorname{Fit} \simeq$ $C_1$ | |
| Radical: | $R \simeq$ $C_{2} \times C_{43740}$ | $G/R \simeq$ $C_1$ | |
| Socle: | $S \simeq$ $C_2\times C_{30}$ | $G/S \simeq$ $C_{1458}$ | |
| 2-Sylow subgroup: | $P_{2} \simeq$ $C_2\times C_4$ | ||
| 3-Sylow subgroup: | $P_{3} \simeq$ $C_{2187}$ | ||
| 5-Sylow subgroup: | $P_{5} \simeq$ $C_5$ |