Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211×C5 |
| direct product | C2×#120×C5⋊D5 |
| Fitting | C2×C52×#120 ⋊ C2 |
| Sylow | C52 ⋊ C22×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×C5⋊D5 |
| commutator, cosocle | C22×C52 | C25 |
| Frattini | C22 | C24×C5⋊D5 |
| Fitting | C2×C52×#120 | C2 |
| socle | C23×C52 | C24 |
| hypercenter | C2×#120 | C5⋊D5 |
| hypocenter | C52 | C22×#120 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
18176 conjugacy classes of subgroups.
392 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5⋊D5×#3484, C2×#120×#1043, #72258310, … |
| maximal normal subgroup of | C5⋊D5×#3484, C2×#120×#1043, #72258310, … |
| maximal quotient of | C2×C5⋊D5×#453, C5⋊D5×#2846 |
Past the SmallGroups library coverage — no SmallGroups id.