Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3672 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#3672 |
| Sylow | C9 ⋊ C22×SD16 |
447 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #11787419, #11787425, #11787561, … |
| maximal normal subgroup of | #11787419, #11787425, #11787561, … |
| maximal quotient of | C22×#63392, C22×#63368, C22×#63367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1776);