Finite Group DatabasebetaFinite Group Databasebeta| order | 23760 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 138240 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C5×C11×C27 |
| multiplicative | (ℤ/27577)ˣ, (ℤ/31165)ˣ, (ℤ/37329)ˣ, (ℤ/39567)ˣ, (ℤ/44565)ˣ, (ℤ/46575)ˣ, (ℤ/47536)ˣ, (ℤ/49005)ˣ, (ℤ/49772)ˣ, (ℤ/52756)ˣ, (ℤ/55154)ˣ, (ℤ/59420)ˣ, (ℤ/62330)ˣ, (ℤ/74658)ˣ, (ℤ/79134)ˣ, (ℤ/89130)ˣ, (ℤ/93150)ˣ, (ℤ/98010)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C9 | C23×C3×C5×C11 |
| socle, prime radical | C23×C3×C5×C11 | C2×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
432 conjugacy classes of subgroups.
23760 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.