Finite Group DatabasebetaFinite Group Databasebeta| order | 13824 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 260919263232 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C3×C43 |
| abelian | C22×C3×C42×C8×C9 |
| multiplicative | (ℤ/37960)ˣ, (ℤ/39520)ˣ, (ℤ/40880)ˣ, (ℤ/41440)ˣ, (ℤ/45552)ˣ, (ℤ/46176)ˣ, (ℤ/52560)ˣ, (ℤ/53280)ˣ, (ℤ/56160)ˣ, (ℤ/56940)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3×C4 | C25×C32 |
| socle, prime radical | C25×C32 | C22×C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
65940 conjugacy classes of subgroups.
13824 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.