Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ C2×C4⋊C8 |
330 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=d,c^2=e,d^2=f,c^a=ce,h^a=h^2,c^b=ce,g^b=g^296 conjugacy classes — view the full character table.
| maximal subgroup of | #11770758, #11770798, #11770868, … |
| maximal normal subgroup of | #11770758, #11770798, #11770868, … |
| maximal quotient of | #11776763, #11776787, #11776815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2213);