Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3774 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#63743 |
| Sylow | C32 ⋊ C2×#107 |
222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #11772503, C4×#63743, #11784478, … |
| maximal normal subgroup of | #11772503, C4×#63743, #11784478, … |
| maximal quotient of | C2×#10590042, #11776902, #11777022, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5392);