Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4×C5×C7 ⋊ C4 |
| Hall | C5×C7 ⋊ #95 |
| Sylow | C7 ⋊ (C2×AGL(1,𝔽5))⋊C4 |
| Sylow | C5 ⋊ C7⋊#95 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^5,5,7|a^2=c,b^2=d,b^a=be,f^a=f^2,g^a=g^6,f^c=f^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #72218096, C22⋊C4×C7⋊AGL(1,𝔽5), AGL(1,𝔽5)×(C2×D7)⋊C4, … |
| maximal normal subgroup of | #72218096, C22⋊C4×C7⋊AGL(1,𝔽5), AGL(1,𝔽5)×(C2×D7)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 289);