Finite Group DatabasebetaFinite Group Databasebeta| order | 11200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 30720 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C4×C7×C16×C25 |
| multiplicative | (ℤ/11413)ˣ, (ℤ/11629)ˣ, (ℤ/11917)ˣ, (ℤ/14005)ˣ, (ℤ/14125)ˣ, (ℤ/22826)ˣ, (ℤ/23258)ˣ, (ℤ/23834)ˣ, (ℤ/28010)ˣ, (ℤ/28250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C5×C8 | C22×C5×C7 |
| socle, prime radical | C22×C5×C7 | C2×C5×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
174 conjugacy classes of subgroups.
11200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.