Finite Group DatabasebetaFinite Group Databasebeta| order | 24246 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C7×C9×C64 (order 8064) · Inn(G) = C1 · Out(G) = C2×C7×C9×C64 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C24246 |
| abelian | C2×C27×C449 |
| multiplicative | (ℤ/24247)ˣ, (ℤ/48494)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C9 | C2×C3×C449 |
| socle, prime radical | C2×C3×C449 | C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16 conjugacy classes of subgroups.
24246 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic12123, C2×D12123 |
| maximal subgroup of | Dic12123, C2×D12123 |
| maximal normal subgroup of | Dic12123, C2×D12123 |
| automorphism group of | C24247 |
| outer automorphism group of | C24247 |
Past the SmallGroups library coverage — no SmallGroups id.