Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3788 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#63767 |
| Fitting | C2×C32×C8 ⋊ C4 |
| Sylow | C32 ⋊ C2×#97 |
222 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 76 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 | #11770728, #11770827, #11772279, … |
| maximal normal subgroup of | #11770728, #11770827, #11772279, … |
| maximal quotient of | C2×#10590168, #11773512, C2×#10590169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5646);