Finite Group DatabasebetaFinite Group Databasebeta| order | 5376 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C28 |
| direct product | D7×C22⋊#997 |
| Fitting, derived | C22×C7×H(5,𝔽2) ⋊ C2×C3 |
| Hall | C22×D7×H(5,𝔽2) ⋊ C3 |
| Sylow | C7 ⋊ C2×C22⋊#997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×C22⋊(C22⋊A4) |
| commutator, Fitting, cosocle, hypocenter | C22×C7×H(5,𝔽2) | C2×C3 |
| socle | C23×C7 | C2×C22⋊A4 |
| LCS | G ▷ C22×C7×H(5,𝔽2) | |
| UCS | C1 ◁ C2 | |
22372 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 22372 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
140 conjugacy classes — view the full character table.
| maximal quotient of | D7×#11710730 |
Past the SmallGroups library coverage — no SmallGroups id.