Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×C7×C8 ⋊ C4 |
| Hall | C5×C7 ⋊ #107 |
| Sylow | C7 ⋊ #3994 |
| Sylow | C5 ⋊ #6392 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^5,5,7|a^2=c,b^2=de,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^6,f^c=f^4118 conjugacy classes — view the full character table.
| maximal subgroup of | #72217752, D8×C7⋊AGL(1,𝔽5), AGL(1,𝔽5)×D56, … |
| maximal normal subgroup of | #72217752, D8×C7⋊AGL(1,𝔽5), AGL(1,𝔽5)×D56, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 277);