Finite Group DatabasebetaFinite Group Databasebeta| order | 26136 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 95040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C4×C9×C121 |
| multiplicative | (ℤ/26899)ˣ, (ℤ/27607)ˣ, (ℤ/28327)ˣ, (ℤ/30499)ˣ, (ℤ/39213)ˣ, (ℤ/39231)ˣ, (ℤ/53798)ˣ, (ℤ/55214)ˣ, (ℤ/56654)ˣ, (ℤ/60998)ˣ, (ℤ/78426)ˣ, (ℤ/78462)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C11 | C22×C32×C11 |
| socle, prime radical | C22×C32×C11 | C2×C3×C11 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
240 conjugacy classes of subgroups.
26136 conjugacy classes. The character table is too large to display.
| automorphism group of | C37×C727, C19×C1453 |
| outer automorphism group of | C37×C727, C19×C1453 |
Past the SmallGroups library coverage — no SmallGroups id.