Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43×C5 |
| direct product | C2×C42×#1044 |
| Fitting | C2×C42×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #1044 |
| commutator, hypocenter | C52 | C2×C43 |
| Frattini | C22 | C23×#1044 |
| Fitting | C2×C42×C52 | C4 |
| socle | C23×C52 | C22×C4 |
| prime radical | C23×C5⋊D5 | C23 |
| cosocle | C22×C5⋊D5 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C42 | |
3042 conjugacy classes of subgroups; only the 798 normal subgroups are shown.
This group has 3042 conjugacy classes of subgroups — too many to draw. Only its 798 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C42×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | C2×C42×D5⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.