Finite Group DatabasebetaFinite Group Databasebeta| order | 10816 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1610219520 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C24×C4×C169 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C13 | C25×C13 |
| socle, prime radical | C25×C13 | C2×C13 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2043 conjugacy classes of subgroups.
10816 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×C8×C169, C23×C42×C169, C25×C4×C169, … |
| maximal normal subgroup of | C24×C8×C169, C23×C42×C169, C25×C4×C169, … |
| maximal quotient of | C24×C8×C169, C23×C42×C169, C25×C4×C169, … |
Past the SmallGroups library coverage — no SmallGroups id.