Finite Group DatabasebetaFinite Group Databasebeta| order | 5408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#88251 |
| Fitting | C2×D4×C132 ⋊ C2 |
| Sylow | C132 ⋊ H(5,𝔽2) |
494 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
1001 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72259301, #72259622 |
| maximal normal subgroup of | #72259301, #72259622 |
Past the SmallGroups library coverage — no SmallGroups id.