Finite Group DatabasebetaFinite Group Databasebeta| order | 24565 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C4×C16×C289 (order 18496) · Inn(G) = C1 · Out(G) = C4×C16×C289 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C24565 |
| abelian | C5×C4913 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C289 | C5×C17 |
| socle, prime radical | C5×C17 | C289 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8 conjugacy classes of subgroups.
24565 conjugacy classes. The character table is too large to display.
| derived subgroup of | D24565 |
| Fitting subgroup of | D24565 |
| maximal subgroup of | D24565 |
| maximal normal subgroup of | D24565 |
Past the SmallGroups library coverage — no SmallGroups id.