Finite Group DatabasebetaFinite Group Databasebeta| order | 17836 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C32×C4×C49 (order 7056) · Inn(G) = C1 · Out(G) = C22×C32×C4×C49 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C17836 |
| abelian | C4×C13×C343 |
| multiplicative | (ℤ/17837)ˣ, (ℤ/35674)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C49 | C2×C7×C13 |
| socle, prime radical | C2×C7×C13 | C2×C49 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
24 conjugacy classes of subgroups.
17836 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic8918, D17836 |
| maximal subgroup of | Dic8918, D17836 |
| maximal normal subgroup of | Dic8918, D17836 |
| automorphism group of | C17837 |
| outer automorphism group of | C17837 |
Past the SmallGroups library coverage — no SmallGroups id.