Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3 |
| direct product | C22×#3752 |
| Fitting | C23×C32×C4 ⋊ C2 |
| Sylow | C32 ⋊ C22×C22⋊C4 |
2022 conjugacy classes of subgroups; only the 559 normal subgroups are shown.
This group has 2022 conjugacy classes of subgroups — too many to draw. Only its 559 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #11773151, #11773162, #11773254, … |
| maximal normal subgroup of | #11773151, #11773162, #11773254, … |
| maximal quotient of | C22×#63658, C2×C4×#3752, C2×#10592654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8140);