Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| isoclinism | isoclinic class of #89167 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#89169 |
| Hall | C5×C11 ⋊ C2×D4 |
| Sylow | C11 ⋊ C2×D20 |
| Sylow | C5 ⋊ C2×C22⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×D11 |
| commutator, cosocle | C2×C5×C11 | C23 |
| Frattini | C2 | C2×D5×D11 |
| Fitting, socle | C22×C5×C11 | C22 |
| hypocenter | C5×C11 | C2×D4 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C22 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 440 |
106 conjugacy classes — view the full character table.
| maximal subgroup of | #13182581, #13182810, #13182814, … |
| maximal normal subgroup of | #13182581, #13182810, #13182814, … |
| maximal quotient of | #13182730, #13182732, #13182733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 171);