Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #5720⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C2×#5720⋊C3 |
| unambiguous semidirect product | (C2×#5720)⋊C3 |
| Fitting | C2×C3×#127 ⋊ C2×C3 |
| derived | C3×C42 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #5720⋊C3 |
| commutator, cosocle, hypocenter | C3×C42 | C23×C3 |
| Frattini | C22 | C22×D3×A4 |
| Fitting | C2×C3×#127 | C2×C3 |
| socle | C23×C3 | C22×A4 |
| LCS | G ▷ C3×C42 | |
| UCS | C1 ◁ C2 | |
623 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 623 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157246);