Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C24 |
| direct product | D5×C5⋊#1020 |
| Fitting, socle | C24×C52 ⋊ C2×D3 |
| derived | C52×C22⋊A4 ⋊ C22 |
| Sylow | C52 ⋊ C2×#1020 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52×C22⋊A4 | C22 |
| Fitting, socle | C24×C52 | C2×D3 |
| LCS | G ▷ C52×C22⋊A4 | |
| UCS | C1 | |
1064 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
104 conjugacy classes — view the full character table.
| maximal subgroup of | D52×#1020, #72258493, #72258517 |
| maximal normal subgroup of | D52×#1020, #72258493, #72258517 |
Past the SmallGroups library coverage — no SmallGroups id.