Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C24×C5×C7 ⋊ C2 |
| Hall | C5×C7 ⋊ #120 |
| Sylow | C7 ⋊ #4099 |
| Sylow | C5 ⋊ #6516 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D35 |
| commutator, socle, cosocle | C22×C5×C7 | C23 |
| Fitting | C24×C5×C7 | C2 |
| hypercenter | C24 | D35 |
| hypocenter | C5×C7 | #120 |
| LCS | G ▷ C22×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C22 ◁ C24 | |
260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^5,5,7|b^a=be,c^a=cd,f^a=f^4,g^a=g^6286 conjugacy classes — view the full character table.
| maximal subgroup of | #72218325, D5×#6516, #120×D35, … |
| maximal normal subgroup of | #72218325, D5×#6516, #120×D35, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 889);