Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| isoclinism | isoclinic class of D5⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×#87830 |
| derived, Sylow | C52 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C23×C42 |
| Frattini | C2 | C23×D5⋊AGL(1,𝔽5) |
| Fitting, socle | C24×C52 | C2×C4 |
| prime radical | C24×C5⋊D5 | C22 |
| cosocle | C2×C5⋊D5 | C25 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C24 | |
7362 conjugacy classes of subgroups; only the 1803 normal subgroups are shown.
This group has 7362 conjugacy classes of subgroups — too many to draw. Only its 1803 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
224 conjugacy classes — view the full character table.
| maximal subgroup of | #72221683, #72221686, C22×C4×#87830, … |
| maximal normal subgroup of | #72221683, #72221686, C22×C4×#87830, … |
| maximal quotient of | #72223261, C23×#11716761, C2×#72221297, … |
Past the SmallGroups library coverage — no SmallGroups id.