Finite Group DatabasebetaFinite Group Databasebeta| order | 27200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 15728640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4×C5 |
| abelian | C2×C4×C52×C8×C17 |
| multiplicative | (ℤ/37675)ˣ, (ℤ/75350)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C23×C52×C17 |
| socle, prime radical | C23×C52×C17 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1296 conjugacy classes of subgroups.
27200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.