Finite Group DatabasebetaFinite Group Databasebeta| order | 10816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#72214198 |
| Fitting | C23×C132 ⋊ C2×C4 |
| Sylow | C132 ⋊ C2×C4×D4 |
1560 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1560 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
244 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72214210, #72259364 |
| maximal normal subgroup of | C2×#72214210, #72259364 |
| maximal quotient of | #72259289 |
Past the SmallGroups library coverage — no SmallGroups id.