Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#63804 |
| Sylow | C32 ⋊ C2×#131 |
566 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #11796056, C4×#63804, #11857282, … |
| maximal normal subgroup of | #11796056, C4×#63804, #11857282, … |
| maximal quotient of | C2×#10590910, C2×#10590908, C2×#10590693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6577);