Finite Group DatabasebetaFinite Group Databasebeta| order | 6912 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 589824 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C8 |
| abelian | C2×C8×C16×C27 |
| multiplicative | (ℤ/13856)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C8×C9 | C23×C3 |
| socle, prime radical | C23×C3 | C4×C8×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
796 conjugacy classes of subgroups.
6912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C8×C27×C32, C2×C162×C27, C4×C8×C16×C27, … |
| maximal normal subgroup of | C2×C8×C27×C32, C2×C162×C27, C4×C8×C16×C27, … |
| maximal quotient of | C2×C8×C27×C32, C2×C162×C27, C4×C8×C16×C27, … |
Past the SmallGroups library coverage — no SmallGroups id.