Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C8×#1043 |
| Fitting | C22×C52×C8 ⋊ C4 |
| derived, Sylow | C52 ⋊ C22×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | #1043 |
| commutator, hypocenter | C52 | C22×C4×C8 |
| Frattini | C4 | C23×#1043 |
| Fitting | C22×C52×C8 | C4 |
| socle | C23×C52 | C42 |
| prime radical | C23×C5⋊D5 | C2×C4 |
| cosocle | C4×C5⋊D5 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C8 | |
3040 conjugacy classes of subgroups; only the 646 normal subgroups are shown.
This group has 3040 conjugacy classes of subgroups — too many to draw. Only its 646 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#97×#1043, C2×#106×#1043, C22×D8×#1043, … |
| maximal normal subgroup of | C2×#97×#1043, C2×#106×#1043, C22×D8×#1043, … |
| maximal quotient of | C8×D4×#1043, C2×M32×#1043 |
Past the SmallGroups library coverage — no SmallGroups id.