Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4×C5 |
| direct product | D3×#11717194 |
| Fitting | C3×C42×C52 ⋊ C22 |
| Hall | C3×C52 ⋊ C2×#127 |
| Sylow | C52 ⋊ D3×#127 |
| Sylow | C3 ⋊ C2×#11717194 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×C5⋊D5 |
| commutator, socle, cosocle | C22×C3×C52 | C24 |
| Fitting | C3×C42×C52 | C22 |
| hypercenter | C42 | D3×C5⋊D5 |
| hypocenter | C3×C52 | C2×#127 |
| LCS | G ▷ C22×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
3984 conjugacy classes of subgroups; only the 614 normal subgroups are shown.
This group has 3984 conjugacy classes of subgroups — too many to draw. Only its 614 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1200 |
618 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#127×C5⋊D5 |
| maximal normal subgroup of | D3×#127×C5⋊D5 |
Past the SmallGroups library coverage — no SmallGroups id.