Finite Group DatabasebetaFinite Group Databasebeta| order | 3360 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | D5×D7×S4 |
| Fitting, socle | C22×C5×C7 ⋊ C22×D3 |
| derived | C5×C7×A4 ⋊ C23 |
| Hall | C5×C7 ⋊ C22×S4 |
| Sylow | C7 ⋊ C2×D5×S4 |
| Sylow | C5 ⋊ C2×D7×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C7×A4 | C23 |
| Fitting, socle | C22×C5×C7 | C22×D3 |
| LCS | G ▷ C5×C7×A4 | |
| UCS | C1 | |
524 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
100 conjugacy classes — view the full character table.
| maximal subgroup of | D5×S4×AGL(1,𝔽7), D7×AGL(1,𝔽5)×S4 |
| maximal normal subgroup of | D5×S4×AGL(1,𝔽7), D7×AGL(1,𝔽5)×S4 |
| maximal quotient of | D5×D7×GL(2,𝔽3) |
Past the SmallGroups library coverage — no SmallGroups id.