Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C22⋊C4×C599 ⋊ C2 |
| Sylow | C599 ⋊ #124 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9584 |
Polycyclic presentation:
2^5,599|b^2=e,c^2=d,b^a=bd,c^a=ce,f^c=f^5983004 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #124×D599, C2×#34062701, #50306417, … |
| maximal normal subgroup of | #124×D599, C2×#34062701, #50306417, … |
| maximal quotient of | #50305754, #50305778, #50305779, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 132);