Finite Group DatabasebetaFinite Group Databasebeta| order | 7040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6553999717171200 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C221 |
| abelian | C27×C5×C11 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
116848 conjugacy classes of subgroups.
7040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C28×C5×C11, C26×C4×C5×C11, C27×C3×C5×C11 |
| maximal normal subgroup of | C28×C5×C11, C26×C4×C5×C11, C27×C3×C5×C11 |
| maximal quotient of | C28×C5×C11, C26×C4×C5×C11, C27×C3×C5×C11 |
Past the SmallGroups library coverage — no SmallGroups id.