Finite Group DatabasebetaFinite Group Databasebeta| order | 28160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2013265920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C42×C8 |
| abelian | C2×C4×C5×C82×C11 |
| multiplicative | (ℤ/54735)ˣ, (ℤ/58384)ˣ, (ℤ/71200)ˣ, (ℤ/72980)ˣ, (ℤ/109470)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C42 | C24×C5×C11 |
| socle, prime radical | C24×C5×C11 | C2×C42 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
7688 conjugacy classes of subgroups.
28160 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.