Finite Group DatabasebetaFinite Group Databasebeta| order | 5600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D7×#87886 |
| Fitting | C22×C52×C7 ⋊ C23 |
| Hall | C52×C7 ⋊ C22×D4 |
| Sylow | C52 ⋊ C2×D4×D7 |
| Sylow | C7 ⋊ C2×#87886 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D52×D7 |
| commutator, socle, cosocle | C2×C52×C7 | C24 |
| Fitting | C22×C52×C7 | C23 |
| hypercenter | C22 | D52×D7 |
| hypocenter | C52×C7 | C22×D4 |
| LCS | G ▷ C2×C52×C7 ▷ C52×C7 | |
| UCS | C1 ◁ C2 ◁ C22 | |
1212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 140 |
230 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#11717375, AGL(1,𝔽7)×#87886 |
| maximal normal subgroup of | D7×#11717375, AGL(1,𝔽7)×#87886 |
Past the SmallGroups library coverage — no SmallGroups id.