Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | A4×#204 |
| unambiguous semidirect product | (C22×#204)⋊C3 |
| Fitting | C22×C3×C8 ⋊ C2×C3 |
174 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#204, #11921800, #11921803, … |
| maximal normal subgroup of | S4×#204, #11921800, #11921803, … |
| maximal quotient of | #79911⋊C3, SL(2,𝔽3)×#204, #79925⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5570);