Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C32 ⋊ C4×C22⋊C4 |
554 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 164 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|a^2=e,b^2=d,c^2=d,c^a=cdf,h^a=h^2,g^b=g^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #11775028, #11775033, #11775035, … |
| maximal normal subgroup of | #11775028, #11775033, #11775035, … |
| maximal quotient of | Dic3×C3⋊#95, #11773163, #11773192, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3119);