Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3×C4 |
| direct product | C2×#10592394 |
| Fitting | C2×C32×C4×C8 ⋊ C2 |
| Sylow | C32 ⋊ C2×#493 |
2280 conjugacy classes of subgroups; only the 537 normal subgroups are shown.
This group has 2280 conjugacy classes of subgroups — too many to draw. Only its 537 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3⋊D3×#493 |
| maximal normal subgroup of | C2×C3⋊D3×#493 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108193);