Finite Group DatabasebetaFinite Group Databasebeta| order | 8000 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C27 |
| direct product | #120×D25⋊C5 |
| Fitting | #120×5−1+2 ⋊ C2 |
| Sylow | 5−1+2 ⋊ C2×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D25⋊C5 |
| commutator, cosocle | C22×C25 | C24×C5 |
| Frattini, socle | C22×C5 | C23×C5×D5 |
| Fitting | #120×5−1+2 | C2 |
| hypercenter | #120 | D25⋊C5 |
| hypocenter | C25 | C2×C5×#120 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ #120 | |
2116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #120×AGL(1,ℤ/25), B(4,𝔽2)×D25⋊C5, #72275816 |
| maximal normal subgroup of | #120×AGL(1,ℤ/25), B(4,𝔽2)×D25⋊C5, #72275816 |
| maximal quotient of | B(4,𝔽2)×D25⋊C5 |
Past the SmallGroups library coverage — no SmallGroups id.