Finite Group DatabasebetaFinite Group Databasebeta| order | 26082 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C23×C3×C11×C27 (order 7128) · Inn(G) = C1 · Out(G) = C23×C3×C11×C27 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C26082 |
| abelian | C2×C7×C23×C81 |
| multiplicative | (ℤ/26083)ˣ, (ℤ/52166)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C27 | C2×C3×C7×C23 |
| socle, prime radical | C2×C3×C7×C23 | C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
40 conjugacy classes of subgroups.
26082 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic13041, C2×D13041 |
| maximal subgroup of | Dic13041, C2×D13041 |
| maximal normal subgroup of | Dic13041, C2×D13041 |
| automorphism group of | C26083 |
| outer automorphism group of | C26083 |
Past the SmallGroups library coverage — no SmallGroups id.