Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3⋊#5935 |
| unambiguous semidirect product | (C2×C3)⋊#5935 |
| Fitting | C2×C3×H(5,𝔽2) ⋊ D3 |
| derived | C3×#997 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊#1020 |
| commutator, cosocle, hypocenter | C3×#997 | C22 |
| Frattini | C2 | C2×C3⋊#1020 |
| Fitting | C2×C3×H(5,𝔽2) | D3 |
| socle | C22×C3 | #1020 |
| LCS | G ▷ C3×#997 | |
| UCS | C1 ◁ C22 | |
770 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#5935, #72215523, #72215563, … |
| maximal normal subgroup of | C2×D3×#5935, #72215523, #72215563, … |
| maximal quotient of | C2×C3⋊(C3⋊#5935), D3×C3⋊#5935, D5×C3⋊#5935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157790);