Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6107⋊C3 |
| Hall | #6107 ⋊ C3 |
| Hall | C13⋊C3 ⋊ Q16 |
| Sylow | C13 ⋊ C3×Q16 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^2,3,2^2,13|a^2=e,b^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^12,d^b=de,f^c=f^331 conjugacy classes — view the full character table.
| maximal subgroup of | #88169⋊C3, #88170⋊C3, Q16×D13⋊C3, … |
| maximal normal subgroup of | #88169⋊C3, #88170⋊C3, Q16×D13⋊C3, … |
| maximal quotient of | #88047⋊C3, #88050⋊C3, #88075⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 22);