Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #120⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#1779⋊C3 |
| unambiguous semidirect product | #1779⋊C32 |
| unambiguous semidirect product | (C3×#1779)⋊C3 |
| Fitting | C3×#1779 ⋊ C3 |
| derived | C24 ⋊ C32×C8 |
| Sylow | #1779 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | #120⋊C3 |
| commutator, hypocenter | C24 | C32×C8 |
| Frattini | C22×C4 | C2×C3×A4 |
| Fitting | C3×#1779 | C3 |
| socle | C23×C3 | C4×A4 |
| prime radical | C2×C3×C22⋊A4 | C4 |
| cosocle | C24×C4 | C2×C32 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C3×C4 | |
380 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153355);