Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#3797 |
| Sylow | C32 ⋊ C23×Q8 |
1818 conjugacy classes of subgroups; only the 608 normal subgroups are shown.
This group has 1818 conjugacy classes of subgroups — too many to draw. Only its 608 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #11773488, #11784661, #11784666, … |
| maximal normal subgroup of | #11773488, #11784661, #11784666, … |
| maximal quotient of | C22×#63883, C22×#63900, C2×C4×#3797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8541);