Finite Group DatabasebetaFinite Group Databasebeta| order | 22848 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 393216 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C4×C7×C8×C17 |
| multiplicative | (ℤ/27811)ˣ, (ℤ/29455)ˣ, (ℤ/33355)ˣ, (ℤ/33565)ˣ, (ℤ/35583)ˣ, (ℤ/35757)ˣ, (ℤ/37167)ˣ, (ℤ/42855)ˣ, (ℤ/42885)ˣ, (ℤ/45712)ˣ, (ℤ/45728)ˣ, (ℤ/47444)ˣ, (ℤ/49556)ˣ, (ℤ/55622)ˣ, (ℤ/57140)ˣ, (ℤ/58910)ˣ, (ℤ/66710)ˣ, (ℤ/67130)ˣ, (ℤ/71166)ˣ, (ℤ/71514)ˣ, (ℤ/74334)ˣ, (ℤ/85710)ˣ, (ℤ/85770)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C23×C3×C7×C17 |
| socle, prime radical | C23×C3×C7×C17 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
22848 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.