Finite Group DatabasebetaFinite Group Databasebeta| order | 24300 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 116640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C3×C25×C81 |
| multiplicative | (ℤ/24613)ˣ, (ℤ/28357)ˣ, (ℤ/36459)ˣ, (ℤ/36693)ˣ, (ℤ/49226)ˣ, (ℤ/56714)ˣ, (ℤ/72918)ˣ, (ℤ/73386)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5×C27 | C22×C32×C5 |
| socle, prime radical | C22×C32×C5 | C5×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
270 conjugacy classes of subgroups.
24300 conjugacy classes. The character table is too large to display.
| automorphism group of | C151×C163 |
| outer automorphism group of | C151×C163 |
Past the SmallGroups library coverage — no SmallGroups id.