Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#63969 |
| Sylow | C32 ⋊ C2×#123 |
750 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#63969, #11802205, #11802217, … |
| maximal normal subgroup of | C4×#63969, #11802205, #11802217, … |
| maximal quotient of | C2×#10591362, C2×#10591373, C2×#10591721, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7374);