Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#3773 |
| Sylow | C32 ⋊ C4×C4⋊C4 |
302 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #11770802, #11771214, #11775099, … |
| maximal normal subgroup of | #11770802, #11771214, #11775099, … |
| maximal quotient of | C4×#63737, #11773194, #11773216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5291);