Finite Group DatabasebetaFinite Group Databasebeta| order | 22392 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 119040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C32×C4×C311 |
| multiplicative | (ℤ/24271)ˣ, (ℤ/26131)ˣ, (ℤ/33597)ˣ, (ℤ/48542)ˣ, (ℤ/52262)ˣ, (ℤ/67194)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C32×C311 |
| socle, prime radical | C22×C32×C311 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
96 conjugacy classes of subgroups.
22392 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C1867 |
| outer automorphism group of | C13×C1867 |
Past the SmallGroups library coverage — no SmallGroups id.