Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C32×C4×D4 ⋊ C2 |
| Sylow | C32 ⋊ #520 |
882 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|b^2=f,d^2=e,c^a=cf,g^a=g^2,h^a=h^2,c^b=cf,d^b=df114 conjugacy classes — view the full character table.
| maximal subgroup of | #11860455, #11860467, #11860501, … |
| maximal normal subgroup of | #11860455, #11860467, #11860501, … |
| maximal quotient of | #11800867, #11800870, #11800900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7899);