Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C22×#3748 |
| Sylow | C32 ⋊ C22×M16 |
894 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #11783078, #11783081, #11783090, … |
| maximal normal subgroup of | #11783078, #11783081, #11783090, … |
| maximal quotient of | C22×#63630, C2×C4×#3748, C22×#63657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8134);