Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C13 ⋊ SD16 |
| Sylow | C13 ⋊ #215 |
| Sylow | C3 ⋊ #6095 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 312 |
Polycyclic presentation:
2^4,3,13|a^2=d,b^2=c,c^2=d,b^a=bc,c^a=cd,f^a=f^12,e^b=e^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6095, #11928393, #11928404, … |
| maximal normal subgroup of | D3×#6095, #11928393, #11928404, … |
| maximal quotient of | #11927976, #11927979, #11927995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 38);