Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊(#120⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C3⋊(#379⋊C3) |
| unambiguous semidirect product | (C2×C3)⋊(#379⋊C3) |
| unambiguous semidirect product | (C2×#5247)⋊C3 |
| derived | C24×C3 ⋊ C2×C3×C4 |
1303 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 1303 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#82612⋊C3, C2×#11920749, C2×#11920748, … |
| maximal normal subgroup of | C2×#82612⋊C3, C2×#11920749, C2×#11920748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155396);