Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#11715653 |
| derived | C22⋊SL(2,𝔽3) ⋊ C22×C4 |
8120 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 8120 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72227571, #72267948 |
| maximal normal subgroup of | C2×#72227571, #72267948 |
| maximal quotient of | #72267948 |
Past the SmallGroups library coverage — no SmallGroups id.