Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×C22⋊C4×D9 |
| Fitting | C2×C9×C22⋊C4 ⋊ C2 |
| Sylow | C9 ⋊ C22×C22⋊C4 |
1011 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 1011 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#323, #11773844, D9×#342, … |
| maximal normal subgroup of | D9×#323, #11773844, D9×#342, … |
| maximal quotient of | C2×D9×#95, C4×C22⋊C4×D9, C2×#10588346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1468);