Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C5×C11 ⋊ #41 |
| Sylow | C11 ⋊ #713 |
| Sylow | C5 ⋊ #4339 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D5×D11 |
| commutator, socle, cosocle | C2×C5×C11 | C23 |
| Fitting | C4×C5×C11 | C22 |
| hypercenter | C4 | D5×D11 |
| hypocenter | C5×C11 | #41 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2 ◁ C4 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 440 |
Polycyclic presentation:
2^4,5,11|a^2=d,b^2=d,c^2=d,c^a=cd,f^a=f^10,e^b=e^4100 conjugacy classes — view the full character table.
| maximal subgroup of | #13182565, #13182566, #13182669, … |
| maximal normal subgroup of | #13182565, #13182566, #13182669, … |
| maximal quotient of | Dic5×Dic22, #13182701, #13182706, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 154);