Finite Group DatabasebetaFinite Group Databasebeta| order | 23688 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C25×C32×C23 (order 6624) · Inn(G) = C1 · Out(G) = C25×C32×C23 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C23688 |
| abelian | C7×C8×C9×C47 |
| multiplicative | (ℤ/23689)ˣ, (ℤ/47378)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C2×C3×C7×C47 |
| socle, prime radical | C2×C3×C7×C47 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
48 conjugacy classes of subgroups.
23688 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic11844, D23688 |
| maximal subgroup of | Dic11844, D23688 |
| maximal normal subgroup of | Dic11844, D23688 |
| automorphism group of | C23689 |
| outer automorphism group of | C23689 |
Past the SmallGroups library coverage — no SmallGroups id.