Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C32×C4⋊C8 ⋊ C2 |
| Sylow | C32 ⋊ C8×D4 |
402 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 125 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=e,c^2=d,d^2=f,b^a=be,g^a=g^2,h^a=h^2,c^b=ce120 conjugacy classes — view the full character table.
| maximal subgroup of | #11771535, #11777131, #11777137, … |
| maximal normal subgroup of | #11771535, #11777131, #11777137, … |
| maximal quotient of | #11777137, #11777171, #11777221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4415);