Finite Group DatabasebetaFinite Group Databasebeta| order | 552 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic6 |
| unambiguous semidirect product | C3⋊(Q8×C23) |
| Hall | C3×C23 ⋊ Q8 |
| Sylow | C3 ⋊ Q8×C23 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 552 |
207 conjugacy classes — view the full character table.
| maximal subgroup of | #11764139, #11764144, #11764145, … |
| maximal normal subgroup of | #11764139, #11764144, #11764145, … |
| maximal quotient of | C23×Dic3⋊C4, C23×C4⋊Dic3, C2×C23×Dic6, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(552, 18);