Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3 |
| direct product | D8×C3⋊(C3⋊C8) |
| Sylow | C32 ⋊ C8×D8 |
588 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #72254907, C8×D8×C3⋊D3, #72254924 |
| maximal normal subgroup of | #72254907, C8×D8×C3⋊D3, #72254924 |
| maximal quotient of | #72254907 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 11151);