Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | Aut(G) = C24×D3×AGL(1,𝔽11) (order 10560) · Inn(G) = C2×D33 · Out(G) = C24×C5 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×C4×C11 ⋊ C2 |
| Hall | C3×C11 ⋊ C22⋊C4 |
| Sylow | C11 ⋊ (C2×D3)⋊C4 |
| Sylow | C3 ⋊ (C2×D11)⋊C4 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^4,3,11|b^2=c,b^a=bd,e^a=e^2,f^a=f^10138 conjugacy classes — view the full character table.
| maximal subgroup of | #11760738, #11760746, #11760769, … |
| maximal normal subgroup of | #11760738, #11760746, #11760769, … |
| maximal quotient of | #11760626, #11760627, #11760630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 73);