Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#63780 |
| Sylow | C32 ⋊ C2×#101 |
302 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | #11772616, #11772617, #11772621, … |
| maximal normal subgroup of | #11772616, #11772617, #11772621, … |
| maximal quotient of | C2×#10590202, C2×#10590203, #11773832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5689);