Finite Group DatabasebetaFinite Group Databasebeta| order | 30960 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 193536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C5×C9×C43 |
| multiplicative | (ℤ/36157)ˣ, (ℤ/40945)ˣ, (ℤ/47841)ˣ, (ℤ/51117)ˣ, (ℤ/51381)ˣ, (ℤ/58185)ˣ, (ℤ/61928)ˣ, (ℤ/63788)ˣ, (ℤ/68156)ˣ, (ℤ/72314)ˣ, (ℤ/81890)ˣ, (ℤ/92892)ˣ, (ℤ/95682)ˣ, (ℤ/102234)ˣ, (ℤ/102762)ˣ, (ℤ/116370)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C3×C5×C43 |
| socle, prime radical | C23×C3×C5×C43 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
30960 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.