Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×Q8×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ SD16 |
| Sylow | C13 ⋊ #215 |
| Sylow | C3 ⋊ #6106 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 312 |
Polycyclic presentation:
2^4,3,13|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×#215, #11928643, D3×#6106, … |
| maximal normal subgroup of | D13×#215, #11928643, D3×#6106, … |
| maximal quotient of | #11928120, #11928121, #11928147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 106);