Finite Group DatabasebetaFinite Group Databasebeta| order | 7155 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2336256 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C33 |
| abelian | C33×C5×C53 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
112 conjugacy classes of subgroups.
7155 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C33×C5×C53, C32×C5×C9×C53, C34×C5×C53 |
| maximal normal subgroup of | C2×C33×C5×C53, C32×C5×C9×C53, C34×C5×C53 |
| maximal quotient of | C2×C33×C5×C53, C32×C5×C9×C53, C34×C5×C53 |
Past the SmallGroups library coverage — no SmallGroups id.