Finite Group DatabasebetaFinite Group Databasebeta| order | 19008 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2211840 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C3×C4×C8×C9×C11 |
| multiplicative | (ℤ/21827)ˣ, (ℤ/21983)ˣ, (ℤ/23051)ˣ, (ℤ/24455)ˣ, (ℤ/29637)ˣ, (ℤ/31239)ˣ, (ℤ/43654)ˣ, (ℤ/43966)ˣ, (ℤ/46102)ˣ, (ℤ/48910)ˣ, (ℤ/59274)ˣ, (ℤ/62478)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C4 | C23×C32×C11 |
| socle, prime radical | C23×C32×C11 | C2×C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1620 conjugacy classes of subgroups.
19008 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C23×C73, C13×C19×C89, C13×C27×C89 |
| outer automorphism group of | C13×C23×C73, C13×C19×C89, C13×C27×C89 |
Past the SmallGroups library coverage — no SmallGroups id.