Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×C7×C22⋊C4 ⋊ C2 |
| Hall | C5×C7 ⋊ #120 |
| Sylow | C7 ⋊ #4028 |
| Sylow | C5 ⋊ #6445 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D35 |
| commutator, socle, cosocle | C22×C5×C7 | C23 |
| Fitting | C5×C7×C22⋊C4 | C2 |
| hypercenter | C22⋊C4 | D35 |
| hypocenter | C5×C7 | #120 |
| LCS | G ▷ C22×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
260 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^5,5,7|c^2=e,c^a=ce,f^a=f^4,g^a=g^6,c^b=cd184 conjugacy classes — view the full character table.
| maximal subgroup of | #72218376, D5×#6445, #120×D35, … |
| maximal normal subgroup of | #72218376, D5×#6445, #120×D35, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 819);