Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C2×C32×C4⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ #539 |
654 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 183 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|c^2=e,d^2=f,b^a=bf,d^a=de,g^a=g^2,h^a=h^2,d^c=df102 conjugacy classes — view the full character table.
| maximal subgroup of | #11778045, #11778057, #11778069, … |
| maximal normal subgroup of | #11778045, #11778057, #11778069, … |
| maximal quotient of | #11802801, #11803026, #11803348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7868);