Finite Group DatabasebetaFinite Group Databasebeta| order | 6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C213×C5 |
| direct product | C5⋊D5×#2846 |
| Fitting | C52×#2846 ⋊ C2 |
| Sylow | C52 ⋊ C2×#2846 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×C5⋊D5 |
| commutator, socle, cosocle | C23×C52 | C25 |
| Fitting | C52×#2846 | C2 |
| hypercenter | #2846 | C5⋊D5 |
| hypocenter | C52 | C2×#2846 |
| LCS | G ▷ C23×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ #2846 | |
131560 conjugacy classes of subgroups; only the 2203 normal subgroups are shown.
This group has 131560 conjugacy classes of subgroups — too many to draw. Only its 2203 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
616 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.