Finite Group DatabasebetaFinite Group Databasebeta| order | 17760 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C42×C8×C9 (order 4608) · Inn(G) = C1 · Out(G) = C22×C42×C8×C9 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C17760 |
| abelian | C3×C5×C32×C37 |
| multiplicative | (ℤ/17761)ˣ, (ℤ/35522)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16 | C2×C3×C5×C37 |
| socle, prime radical | C2×C3×C5×C37 | C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
48 conjugacy classes of subgroups.
17760 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic8880, D17760 |
| maximal subgroup of | Dic8880, D17760 |
| maximal normal subgroup of | Dic8880, D17760 |
| automorphism group of | C17761 |
| outer automorphism group of | C17761 |
Past the SmallGroups library coverage — no SmallGroups id.