Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C4×#1043 |
| Fitting | C23×C4×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #1043 |
| commutator, hypocenter | C52 | C23×C42 |
| Frattini | C2 | C24×#1043 |
| Fitting | C23×C4×C52 | C4 |
| socle | C24×C52 | C2×C4 |
| prime radical | C24×C5⋊D5 | C22 |
| cosocle | C2×C5⋊D5 | C25 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23×C4 | |
12000 conjugacy classes of subgroups; only the 2326 normal subgroups are shown.
This group has 12000 conjugacy classes of subgroups — too many to draw. Only its 2326 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D4×#1043, #525×#1043, #72223273, … |
| maximal normal subgroup of | C23×D4×#1043, #525×#1043, #72223273, … |
| maximal quotient of | C4×#41×#1043, #518×#1043, C2×C4×D4×#1043, … |
Past the SmallGroups library coverage — no SmallGroups id.