Finite Group DatabasebetaFinite Group Databasebeta| order | 19232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C601 ⋊ SD32 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9616 |
Polycyclic presentation:
2^5,601|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^600,c^b=cd,d^b=de2111 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD32×D601, C2×#34063769, #50309105, … |
| maximal normal subgroup of | SD32×D601, C2×#34063769, #50309105, … |
| maximal quotient of | #50308477, #50308479, #50308503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19232, 90);