Finite Group DatabasebetaFinite Group Databasebeta| order | 22272 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 22020096 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C3×C4×C16×C29 |
| multiplicative | (ℤ/35105)ˣ, (ℤ/39117)ˣ, (ℤ/45135)ˣ, (ℤ/47464)ˣ, (ℤ/49088)ˣ, (ℤ/52156)ˣ, (ℤ/67008)ˣ, (ℤ/70210)ˣ, (ℤ/71196)ˣ, (ℤ/78234)ˣ, (ℤ/90270)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C24×C3×C29 |
| socle, prime radical | C24×C3×C29 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2044 conjugacy classes of subgroups.
22272 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.