Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C23×C3×D12 |
| Fitting | C23×C32×C4 ⋊ C2 |
| Sylow | C32 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C3 | C2×D3 |
| commutator, cosocle | C2×C3 | C25×C3 |
| Frattini | C2 | C24×C3×D3 |
| Fitting | C23×C32×C4 | C2 |
| socle | C24×C32 | C22 |
| hypercenter | C23×C3×C4 | D3 |
| hypocenter | C3 | C23×C3×D4 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C24×C3 ◁ C23×C3×C4 | |
2842 conjugacy classes of subgroups; only the 1086 normal subgroups are shown.
This group has 2842 conjugacy classes of subgroups — too many to draw. Only its 1086 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#69426, #11773285, C3×#69988, … |
| maximal normal subgroup of | C3×#69426, #11773285, C3×#69988, … |
| maximal quotient of | C23×C3×(C2×D3)⋊C4, C23×C3×C4⋊Dic3, C22×C3×C4×D12, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8607);