Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C13 ⋊ Q16 |
| Sylow | C13 ⋊ #216 |
| Sylow | C3 ⋊ #6107 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 624 |
Polycyclic presentation:
2^4,3,13|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^12,c^b=cd102 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#216, #11928649, D3×#6107, … |
| maximal normal subgroup of | D13×#216, #11928649, D3×#6107, … |
| maximal quotient of | #11928119, #11928122, #11928147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 107);