Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×C7×Q8 ⋊ C2 |
| Hall | C5×C7 ⋊ 2−1+4 |
| Sylow | C7 ⋊ #4147 |
| Sylow | C5 ⋊ #6551 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D35 |
| commutator, socle, cosocle | C2×C5×C7 | C24 |
| Fitting | C2×C5×C7×Q8 | C2 |
| hypercenter | C2×Q8 | D35 |
| hypocenter | C5×C7 | 2−1+4 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
292 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
Polycyclic presentation:
2^5,5,7|b^2=e,c^2=e,d^a=de,f^a=f^4,g^a=g^6,c^b=ce187 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1066);