Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C42×#1043 |
| Fitting | C2×C42×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #1043 |
| commutator, hypocenter | C52 | C2×C43 |
| Frattini | C22 | C23×#1043 |
| 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 | |
5088 conjugacy classes of subgroups; only the 1014 normal subgroups are shown.
This group has 5088 conjugacy classes of subgroups — too many to draw. Only its 1014 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 | C4×M16×#1043, C2×#127×#1043, #532×#1043, … |
| maximal normal subgroup of | C4×M16×#1043, C2×#127×#1043, #532×#1043, … |
| maximal quotient of | C4×M16×#1043, C42×D3×#1043, C2×#97×#1043, … |
Past the SmallGroups library coverage — no SmallGroups id.