Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#11717477 |
| Fitting | C22×C52×D4 ⋊ C22 |
| Sylow | C52 ⋊ C23×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D52 |
| commutator, cosocle | C2×C52 | C26 |
| Frattini | C2 | C24×D52 |
| Fitting | C22×C52×D4 | C22 |
| socle | C23×C52 | C24 |
| hypercenter | C22×D4 | D52 |
| hypocenter | C52 | C23×#41 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
14402 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#13107568 |
| maximal normal subgroup of | C22×#13107568 |
Past the SmallGroups library coverage — no SmallGroups id.