Finite Group DatabasebetaFinite Group Databasebeta| order | 27264 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C23×C5×C7×C32 (order 8960) · Inn(G) = C1 · Out(G) = C23×C5×C7×C32 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C27264 |
| abelian | C3×C71×C128 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C64 | C2×C3×C71 |
| socle, prime radical | C2×C3×C71 | C64 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
32 conjugacy classes of subgroups.
27264 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic13632, D27264 |
| maximal subgroup of | Dic13632, D27264 |
| maximal normal subgroup of | Dic13632, D27264 |
Past the SmallGroups library coverage — no SmallGroups id.