Finite Group DatabasebetaFinite Group Databasebeta| order | 6723 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1912896 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C33 |
| abelian | C32×C9×C83 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C3 | C33×C83 |
| socle | C33×C83 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
100 conjugacy classes of subgroups.
6723 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C83×#6855, C83×C32⋊C27, C83×#6867, … |
| maximal normal subgroup of | C83×#6855, C83×C32⋊C27, C83×#6867, … |
| maximal quotient of | C3×C92×C83, C3×C32⋊C9×C83, C3×C9⋊C9×C83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6723, 11);