Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C2×C32×D4 ⋊ C4 |
| Sylow | C32 ⋊ #518 |
574 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^6,3^2|a^2=e,d^a=df,g^a=gh,h^a=gh^2,c^b=cf,g^e=g^2,h^e=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #11786580, #11786597, #11787071, … |
| maximal normal subgroup of | #11786580, #11786597, #11787071, … |
| maximal quotient of | #11800858, #11800879, #11800911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8524);