Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C32 ⋊ C4×M16 |
304 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|b^2=d,c^2=e,d^2=f,b^a=bf,h^a=h^2,c^b=cf,g^b=g^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #11775714, #11775716, #11775717, … |
| maximal normal subgroup of | #11775714, #11775716, #11775717, … |
| maximal quotient of | #11773554, #11773615, #11773667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2216);