Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C599 ⋊ C22⋊Q8 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9584 |
Polycyclic presentation:
2^5,599|a^2=d,b^2=d,b^a=bd,c^a=ce,f^b=f^5983004 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊Q8×D599, C2×#34062692, #50306396, … |
| maximal normal subgroup of | C22⋊Q8×D599, C2×#34062692, #50306396, … |
| maximal quotient of | #50305748, #50305762, #50305765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 123);