This group is not stored in the database. However, basic information about the group, computed on the fly, is listed below.
Group information
Description: | $C_{6} \times C_{468}$ | |
Order: | \(2808\)\(\medspace = 2^{3} \cdot 3^{3} \cdot 13 \) | |
Exponent: | \(468\)\(\medspace = 2^{2} \cdot 3^{2} \cdot 13 \) | |
Automorphism group: | Group of order 10368 | |
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 | 6 | 9 | 12 | 13 | 18 | 26 | 36 | 39 | 52 | 78 | 117 | 156 | 234 | 468 | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Elements | 1 | 3 | 8 | 4 | 24 | 18 | 32 | 12 | 54 | 36 | 72 | 96 | 48 | 288 | 216 | 384 | 648 | 864 | 2808 | |
Conjugacy classes | 1 | 3 | 8 | 4 | 24 | 18 | 32 | 12 | 54 | 36 | 72 | 96 | 48 | 288 | 216 | 384 | 648 | 864 | 2808 | |
Divisions | data not computed | |||||||||||||||||||
Autjugacy classes | data not computed |
Dimension | 1 | |
---|---|---|
Irr. complex chars. | 2808 | 2808 |
Constructions
Rank: | $2$ |
Inequivalent generating pairs: | not computed |
Homology
Primary decomposition: | $C_{2} \times C_{4} \times C_{3} \times C_{9} \times C_{13}$ |
Subgroups
Center: | $Z \simeq$ $C_{6} \times C_{468}$ | $G/Z \simeq$ $C_1$ | |
Commutator: | $G' \simeq$ $C_1$ | $G/G' \simeq$ $C_{6} \times C_{468}$ | |
Frattini: | $\Phi \simeq$ $C_6$ | $G/\Phi \simeq$ $C_6\times C_{78}$ | |
Fitting: | $\operatorname{Fit} \simeq$ $C_{6} \times C_{468}$ | $G/\operatorname{Fit} \simeq$ $C_1$ | |
Radical: | $R \simeq$ $C_{6} \times C_{468}$ | $G/R \simeq$ $C_1$ | |
Socle: | $S \simeq$ $C_6\times C_{78}$ | $G/S \simeq$ $C_6$ | |
2-Sylow subgroup: | $P_{2} \simeq$ $C_2\times C_4$ | ||
3-Sylow subgroup: | $P_{3} \simeq$ $C_3\times C_9$ | ||
13-Sylow subgroup: | $P_{13} \simeq$ $C_{13}$ |