Finite Group DatabasebetaFinite Group Databasebeta| order | 19008 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 368640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C8×C11×C27 |
| multiplicative | (ℤ/29103)ˣ, (ℤ/35655)ˣ, (ℤ/36045)ˣ, (ℤ/38032)ˣ, (ℤ/38804)ˣ, (ℤ/47540)ˣ, (ℤ/58206)ˣ, (ℤ/71310)ˣ, (ℤ/72090)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C9 | C23×C3×C11 |
| socle, prime radical | C23×C3×C11 | C2×C4×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
19008 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.