Finite Group DatabasebetaFinite Group Databasebeta| order | 14400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1981808640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C43×C5 |
| abelian | C32×C43×C52 |
| multiplicative | (ℤ/19825)ˣ, (ℤ/39650)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23 | C23×C32×C52 |
| socle, prime radical | C23×C32×C52 | C23 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6192 conjugacy classes of subgroups.
14400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C42×C52×C8, C2×C32×C43×C52 |
| maximal normal subgroup of | C32×C42×C52×C8, C2×C32×C43×C52 |
| maximal quotient of | C32×C42×C52×C8, C2×C32×C43×C52 |
Past the SmallGroups library coverage — no SmallGroups id.