Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 35389440 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4×C5 |
| abelian | C2×C32×C42×C52 |
| multiplicative | (ℤ/8723)ˣ, (ℤ/9455)ˣ, (ℤ/10075)ˣ, (ℤ/10675)ˣ, (ℤ/13725)ˣ, (ℤ/17446)ˣ, (ℤ/18910)ˣ, (ℤ/20150)ˣ, (ℤ/21350)ˣ, (ℤ/27450)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C32×C52 |
| socle, prime radical | C23×C32×C52 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2592 conjugacy classes of subgroups.
7200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.