Finite Group DatabasebetaFinite Group Databasebeta| order | 24336 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 89856 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C42×C9×C169 |
| multiplicative | (ℤ/25049)ˣ, (ℤ/50098)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, socle, prime radical, cosocle | C22×C3×C13 | C22×C3×C13 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
135 conjugacy classes of subgroups.
24336 conjugacy classes. The character table is too large to display.
| automorphism group of | C37×C677 |
| outer automorphism group of | C37×C677 |
Past the SmallGroups library coverage — no SmallGroups id.