Finite Group DatabasebetaFinite Group Databasebeta| order | 23664 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 14336 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C8×C17×C29 |
| multiplicative | (ℤ/23999)ˣ, (ℤ/24131)ˣ, (ℤ/35499)ˣ, (ℤ/47332)ˣ, (ℤ/47998)ˣ, (ℤ/48262)ˣ, (ℤ/70998)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C22×C3×C17×C29 |
| socle, prime radical | C22×C3×C17×C29 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
88 conjugacy classes of subgroups.
23664 conjugacy classes. The character table is too large to display.
| automorphism group of | C103×C233, C59×C409 |
| outer automorphism group of | C103×C233, C59×C409 |
Past the SmallGroups library coverage — no SmallGroups id.