Finite Group DatabasebetaFinite Group Databasebeta| order | 24192 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 331776 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C4 |
| abelian | C3×C4×C7×C9×C32 |
| multiplicative | (ℤ/24901)ˣ, (ℤ/26221)ˣ, (ℤ/49802)ˣ, (ℤ/52442)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C16 | C22×C32×C7 |
| socle, prime radical | C22×C32×C7 | C2×C3×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
720 conjugacy classes of subgroups.
24192 conjugacy classes. The character table is too large to display.
| automorphism group of | C37×C673 |
| outer automorphism group of | C37×C673 |
Past the SmallGroups library coverage — no SmallGroups id.