Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3774 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#3776 |
| Sylow | C32 ⋊ C4×Q16 |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #11771634, C8×#3776, #11777247, … |
| maximal normal subgroup of | #11771634, C8×#3776, #11777247, … |
| maximal quotient of | C8×#3776, #11777555, #11777862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5326);