Finite Group DatabasebetaFinite Group Databasebeta| order | 1104 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×Q8×C23 ⋊ C2 |
| Hall | C3×C23 ⋊ SD16 |
| Sylow | C23 ⋊ #215 |
| Sylow | C3 ⋊ #67274 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 552 |
Polycyclic presentation:
2^4,3,23|b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^22,c^b=cd177 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1104, 76);