Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #63653 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C4×#63653 |
| Fitting | C32×C4×D8 ⋊ C2 |
| Sylow | C32 ⋊ C4×D16 |
522 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C3⋊D3×D16, #72254921, #72254924 |
| maximal normal subgroup of | C4×C3⋊D3×D16, #72254921, #72254924 |
| maximal quotient of | #72254948 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 31632);