Finite Group DatabasebetaFinite Group Databasebeta| order | 11872 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C3×C4×C8×C13 (order 4992) · Inn(G) = C1 · Out(G) = C22×C3×C4×C8×C13 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C11872 |
| abelian | C7×C32×C53 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16 | C2×C7×C53 |
| socle, prime radical | C2×C7×C53 | C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
24 conjugacy classes of subgroups.
11872 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic11872, D23744 |
| maximal subgroup of | C7×C53×C64, C2×C7×C32×C53, D11872, … |
| maximal normal subgroup of | C7×C53×C64, C2×C7×C32×C53, D11872, … |
| maximal quotient of | C7×C53×C64, C2×C7×C32×C53 |
Past the SmallGroups library coverage — no SmallGroups id.