Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | Aut(G) = D3×#120×AGL(1,𝔽11) (order 21120) · Inn(G) = C2×D33 · Out(G) = C22×C5×D4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic33 |
| Hall | C3×C11 ⋊ C4⋊C4 |
| Sylow | C11 ⋊ C4⋊Dic3 |
| Sylow | C3 ⋊ C4⋊Dic11 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 528 |
Polycyclic presentation:
2^4,3,11|a^2=c,b^2=d,b^a=bd,e^a=e^2,f^a=f^10138 conjugacy classes — view the full character table.
| maximal subgroup of | #11760502, #11760504, #11760508, … |
| maximal normal subgroup of | #11760502, #11760504, #11760508, … |
| maximal quotient of | C4⋊(C3⋊(C11⋊C8)), #11760637, #11760638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 72);