Finite Group DatabasebetaFinite Group Databasebeta| order | 15080 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 225792 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C5×C13×C29 |
| multiplicative | (ℤ/23187)ˣ, (ℤ/30916)ˣ, (ℤ/46374)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
15080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×C5×C13×C29, C22×C4×C5×C13×C29 |
| maximal normal subgroup of | C24×C5×C13×C29, C22×C4×C5×C13×C29 |
| maximal quotient of | C24×C5×C13×C29, C22×C4×C5×C13×C29 |
Past the SmallGroups library coverage — no SmallGroups id.