Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #63546 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#63548 |
| Sylow | C32 ⋊ C2×SD32 |
210 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #11797670, C4×#63548, #11797679, … |
| maximal normal subgroup of | #11797670, C4×#63548, #11797679, … |
| maximal quotient of | C2×#10589115, C2×#10589119, C2×#10589141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2519);