Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×C4×#226 |
151 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 151 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×#226, #226⋊(C3⋊C8), #11920522, … |
| maximal normal subgroup of | C3⋊C8×#226, #226⋊(C3⋊C8), #11920522, … |
| maximal quotient of | C3×C8×#226, C3×#73010, C3×C4×#859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5455);