Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C13 ⋊ M16 |
| Sylow | C13 ⋊ #208 |
| Sylow | C3 ⋊ #6122 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
Polycyclic presentation:
2^4,3,13|a^2=c,c^2=d,b^a=bd,e^a=e^2,f^a=f^5,f^c=f^1254 conjugacy classes — view the full character table.
| maximal subgroup of | #11928221, #11928222, #11928375, … |
| maximal normal subgroup of | #11928221, #11928222, #11928375, … |
| maximal quotient of | #11928371, #11928374, #11928382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 165);