Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C599 ⋊ C2 |
| Sylow | C599 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9584 |
Polycyclic presentation:
2^5,599|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^598,d^b=de,f^c=f^5982104 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #137×D599, C2×#34062747, #50306687, … |
| maximal normal subgroup of | #137×D599, C2×#34062747, #50306687, … |
| maximal quotient of | #50305890, #50305897, #50305931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 178);