Finite Group DatabasebetaFinite Group Databasebeta| order | 18720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6193152 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C4×C5×C9×C13 |
| multiplicative | (ℤ/33231)ˣ, (ℤ/37335)ˣ, (ℤ/38776)ˣ, (ℤ/39824)ˣ, (ℤ/44308)ˣ, (ℤ/46840)ˣ, (ℤ/49780)ˣ, (ℤ/56184)ˣ, (ℤ/56208)ˣ, (ℤ/56592)ˣ, (ℤ/58164)ˣ, (ℤ/62964)ˣ, (ℤ/66462)ˣ, (ℤ/70260)ˣ, (ℤ/70740)ˣ, (ℤ/74670)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C24×C3×C5×C13 |
| socle, prime radical | C24×C3×C5×C13 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1416 conjugacy classes of subgroups.
18720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.