Finite Group DatabasebetaFinite Group Databasebeta| order | 18432 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3145728 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C4×C256 |
| multiplicative | (ℤ/23387)ˣ, (ℤ/26915)ˣ, (ℤ/29991)ˣ, (ℤ/30069)ˣ, (ℤ/34605)ˣ, (ℤ/39988)ˣ, (ℤ/46774)ˣ, (ℤ/53830)ˣ, (ℤ/59982)ˣ, (ℤ/60138)ˣ, (ℤ/69210)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C128 | C23×C32 |
| socle, prime radical | C23×C32 | C2×C128 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1296 conjugacy classes of subgroups.
18432 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.