Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D32⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D32⋊D3 |
| Fitting, socle | C22×C33 ⋊ D4 |
| Sylow | C33 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D32⋊D3 |
| commutator, cosocle | C3×C3⋊D3 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C33 | D4 |
| hypocenter | C33 | C22×D4 |
| LCS | G ▷ C3×C3⋊D3 ▷ C33 | |
| UCS | C1 ◁ C22 | |
804 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 804 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #13165389, #13165390, #13165415, … |
| maximal normal subgroup of | #13165389, #13165390, #13165415, … |
| maximal quotient of | C2×#11724298, C2×#11724299, #13181060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4700);