Finite Group DatabasebetaFinite Group Databasebeta| order | 28320 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 712704 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C42×C5×C59 |
| multiplicative | (ℤ/38995)ˣ, (ℤ/41335)ˣ, (ℤ/46059)ˣ, (ℤ/53115)ˣ, (ℤ/53145)ˣ, (ℤ/53175)ˣ, (ℤ/56656)ˣ, (ℤ/61412)ˣ, (ℤ/70820)ˣ, (ℤ/70900)ˣ, (ℤ/77990)ˣ, (ℤ/82670)ˣ, (ℤ/92118)ˣ, (ℤ/106230)ˣ, (ℤ/106290)ˣ, (ℤ/106350)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C3×C5×C59 |
| socle, prime radical | C23×C3×C5×C59 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
432 conjugacy classes of subgroups.
28320 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.