Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×#626 |
| Sylow | C32 ⋊ C8×D4 |
306 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11797443, #11797444, C16×#626, … |
| maximal normal subgroup of | #11797443, #11797444, C16×#626, … |
| maximal quotient of | C8×#3714, C8×#3717, C8×#3716, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2601);