Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C4⋊(C3⋊Dic3) |
| Sylow | C32 ⋊ C22×C4⋊C4 |
1254 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #11773201, #11773204, #11773212, … |
| maximal normal subgroup of | #11773201, #11773204, #11773212, … |
| maximal quotient of | C22×#63658, C2×C4×C4⋊(C3⋊Dic3), C2×#10592911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8138);