Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #63734 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#63735 |
| Sylow | C32 ⋊ C2×SD32 |
158 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#63735, #11797692, #11797767, … |
| maximal normal subgroup of | C4×#63735, #11797692, #11797767, … |
| maximal quotient of | C2×#10590061, C2×#10590062, C2×#10590069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5217);