Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×C7×C8 ⋊ C22 |
| Hall | C5×C7 ⋊ C2×D8 |
| Sylow | C7 ⋊ D5×D8 |
| Sylow | C5 ⋊ D7×D8 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^5,5,7|c^2=de,d^2=e,c^a=cd,d^a=de,g^a=g^6,c^b=cd,d^b=de,f^b=f^497 conjugacy classes — view the full character table.
| maximal subgroup of | #72217934, D5×D7×D8, #72218482, … |
| maximal normal subgroup of | #72217934, D5×D7×D8, #72218482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 312);