Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3774 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#63733 |
| Sylow | C32 ⋊ C2×#108 |
174 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #11772434, #11772462, #11772524, … |
| maximal normal subgroup of | #11772434, #11772462, #11772524, … |
| maximal quotient of | C2×#10590041, C2×#10590042, #11776821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5211);