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 ⋊ #405 |
298 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 136 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=e,b^2=d,d^2=f,c^a=cf,h^a=h^2,c^b=cf,g^b=g^296 conjugacy classes — view the full character table.
| maximal subgroup of | #11783537, #11783540, #11783842, … |
| maximal normal subgroup of | #11783537, #11783540, #11783842, … |
| maximal quotient of | #11773549, #11773578, #11773610, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2939);