Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C9 |
| direct product | C2×#13046806 |
| Fitting | C2×D4×C92 ⋊ C2 |
| Sylow | C92 ⋊ C2×D8 |
874 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1296 |
414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D8×C9⋊D9, #72254558, #72254568, … |
| maximal normal subgroup of | C2×D8×C9⋊D9, #72254558, #72254568, … |
Past the SmallGroups library coverage — no SmallGroups id.