Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C2×#13106618 |
| Fitting | C25×C52 ⋊ C22 |
| Sylow | C52 ⋊ C22×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D52 |
| commutator, cosocle | C22×C52 | C25 |
| Frattini | C22 | C23×D52 |
| Fitting | C25×C52 | C22 |
| socle | C23×C52 | C24 |
| hypercenter | C25 | D52 |
| hypocenter | C52 | C22×#120 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C25 | |
14738 conjugacy classes of subgroups; only the 820 normal subgroups are shown.
This group has 14738 conjugacy classes of subgroups — too many to draw. Only its 820 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
296 conjugacy classes. The character table is too large to display.
| maximal quotient of | #72223291, #72223374 |
Past the SmallGroups library coverage — no SmallGroups id.