Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C541 ⋊ C4 |
| Sylow | C541 ⋊ #99 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
Polycyclic presentation:
2^5,541|a^2=d,b^a=bc,c^a=ce,f^a=f^52,d^b=de,f^b=f^540,f^d=f^5401091 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46831079, #46831080, #46831081, … |
| maximal normal subgroup of | #46831079, #46831080, #46831081, … |
| maximal quotient of | #46831019, #46831020, #46831027, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 205);