Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#13049781 |
| Fitting, socle | C2×C34 ⋊ C4⋊C4 |
| Sylow | C34 ⋊ C2×C4⋊C4 |
520 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | #72269110, C2×#72220430 |
| maximal normal subgroup of | #72269110, C2×#72220430 |
| maximal quotient of | #72269081 |
Past the SmallGroups library coverage — no SmallGroups id.