Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#10593663 |
| Fitting | C2×C3×H(5,𝔽2) ⋊ D3 |
812 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊SO+(4,𝔽3), C2×D3×#5429, #72242450, … |
| maximal normal subgroup of | C2×D3×#5429, #72242450, #72242452, … |
| maximal quotient of | C2×#13147078, C2×#13147076, C2×C3×#10593663 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157085);