Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×D4×C11 ⋊ C2 |
| Hall | C5×C11 ⋊ #41 |
| Sylow | C11 ⋊ #711 |
| Sylow | C5 ⋊ #4341 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D55 |
| commutator, socle, cosocle | C2×C5×C11 | C23 |
| Fitting | C5×D4×C11 | C2 |
| hypercenter | D4 | D55 |
| hypocenter | C5×C11 | #41 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2 ◁ D4 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 440 |
Polycyclic presentation:
2^4,5,11|b^2=d,c^a=cd,e^a=e^4,f^a=f^10,c^b=cd145 conjugacy classes — view the full character table.
| maximal subgroup of | #13182899, #13182905, #13182914, … |
| maximal normal subgroup of | #13182899, #13182905, #13182914, … |
| maximal quotient of | #13183176, #13183177, #13183178, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 201);