Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C32×C4 ⋊ D4 |
| Sylow | C32 ⋊ #386 |
470 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|c^2=e,b^a=bd,g^a=g^2,c^b=cf,g^b=h,h^b=g,g^d=g^2,h^d=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10593453, #11801555, C4×#64241, … |
| maximal normal subgroup of | C2×#10593453, #11801555, C4×#64241, … |
| maximal quotient of | D32⋊#95, #11773250, #11773270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5335);