Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C9 ⋊ #405 |
195 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 117 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|a^2=d,c^2=e,e^2=f,g^3=h^2,b^a=bf,g^a=g^2h,h^a=h^2168 conjugacy classes — view the full character table.
| maximal subgroup of | #11772321, #11772327, #11772343, … |
| maximal normal subgroup of | #11772321, #11772327, #11772343, … |
| maximal quotient of | C8×#3667, #11773560, #11773592, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 664);