Finite Group DatabasebetaFinite Group Databasebeta| order | 7857 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C3×C27×C32 (order 5184) · Inn(G) = C1 · Out(G) = C2×C3×C27×C32 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C7857 |
| abelian | C81×C97 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C27 | C3×C97 |
| socle | C3×C97 | C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
10 conjugacy classes of subgroups.
7857 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7857, 1);