Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C32×#117 ⋊ C2 |
| Sylow | C32 ⋊ C4×#41 |
930 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 275 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|b^2=f,d^2=e,c^a=cf,g^a=g^2,h^a=h^2,d^c=df120 conjugacy classes — view the full character table.
| maximal subgroup of | #11774238, #11774275, #11774614, … |
| maximal normal subgroup of | #11774238, #11774275, #11774614, … |
| maximal quotient of | #11800755, #117×C3⋊Dic3, C4×#64090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7875);