Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C2×C11×Dic6 |
| unambiguous semidirect product | (C2×C3)⋊(Q8×C11) |
| Hall | C3×C11 ⋊ C2×Q8 |
| Sylow | C3 ⋊ C2×Q8×C11 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 528 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | #11760499, #11760509, #11760510, … |
| maximal normal subgroup of | #11760499, #11760509, #11760510, … |
| maximal quotient of | C4×C11×Dic6, C11×#869, C11×#870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 136);