Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#3417⋊C3 |
| unambiguous semidirect product | #3417⋊C32 |
| unambiguous semidirect product | (C3×#3417)⋊C3 |
| Fitting | C3×#3417 ⋊ C3 |
| Sylow | #3417 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | A4×D8 |
| commutator, cosocle | #131 | C22×C32 |
| Frattini | C8 | C22×C3×A4 |
| Fitting | C3×#3417 | C3 |
| hypercenter | C3×D16 | A4 |
| hypocenter | Q8 | C32×D8 |
| LCS | G ▷ #131 ▷ #41 ▷ Q8 | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×D16 | |
250 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153645);