Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C541 ⋊ C2 |
| Sylow | C541 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^5,541|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^540,d^b=de,f^c=f^5401901 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #137×D541, C2×#31772660, #46830972, … |
| maximal normal subgroup of | #137×D541, C2×#31772660, #46830972, … |
| maximal quotient of | #46830175, #46830182, #46830216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 178);