Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | Q8×C4⋊(C3⋊D3) |
| Fitting | C32×C4×Q8 ⋊ C2 |
| Sylow | C32 ⋊ D4×Q8 |
840 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | #11779199, #11779211, #11779223, … |
| maximal normal subgroup of | #11779199, #11779211, #11779223, … |
| maximal quotient of | Q8×#3752, C4⋊C4×C4⋊(C3⋊D3), Q8×C4⋊(C3⋊Dic3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7928);