Finite Group DatabasebetaFinite Group Databasebeta| order | 17504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C547 ⋊ #126 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8752 |
Polycyclic presentation:
2^5,547|b^2=de,c^2=d,b^a=bd,c^a=ce,f^c=f^5462744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D547, C2×#31775995, #46855528, … |
| maximal normal subgroup of | #126×D547, C2×#31775995, #46855528, … |
| maximal quotient of | #46854868, #46854883, #46854886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17504, 139);