Finite Group DatabasebetaFinite Group Databasebeta| order | 5376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C210 |
| direct product | ΓL(1,𝔽8)×#15947 |
| Fitting, Hall | C7×#15947 ⋊ C3 |
| Sylow | C7 ⋊ C3×#15947 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C24×ΓL(1,𝔽8) |
| commutator, socle, cosocle | C24×C7 | C24×C3 |
| Fitting | C7×#15947 | C3 |
| hypercenter | #15947 | ΓL(1,𝔽8) |
| hypocenter | C7 | C3×#15947 |
| LCS | G ▷ C24×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ #15947 | |
12292 conjugacy classes of subgroups; only the 741 normal subgroups are shown.
This group has 12292 conjugacy classes of subgroups — too many to draw. Only its 741 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽7)×#15947 |
| maximal normal subgroup of | AGL(1,𝔽7)×#15947 |
Past the SmallGroups library coverage — no SmallGroups id.