Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5971968 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C9 |
| abelian | C22×C92×C32 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32×C16 | C23×C32 |
| socle, prime radical | C23×C32 | C32×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1380 conjugacy classes of subgroups.
10368 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C92×C64, C2×C4×C92×C32, C23×C92×C32, … |
| maximal normal subgroup of | C22×C92×C64, C2×C4×C92×C32, C23×C92×C32, … |
| maximal quotient of | C22×C92×C64, C2×C4×C92×C32, C23×C92×C32, … |
Past the SmallGroups library coverage — no SmallGroups id.