Finite Group DatabasebetaFinite Group Databasebeta| order | 5832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#72221853 |
| Fitting | C2×#10624704 ⋊ C22 |
| derived | #6873 ⋊ C23×C3 |
| Sylow | #10624704 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72221853 |
| commutator, cosocle, hypocenter | #6873 | C23×C3 |
| Frattini | C3×C9 | C2×C3×D32 |
| Fitting | C2×#10624704 | C22 |
| socle | C2×C3 | C3×((C3⋊D3)⋊C9)⋊C2 |
| LCS | G ▷ #6873 | |
| UCS | C1 ◁ C2 | |
664 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
138 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221857, C2×#72221870 |
| maximal normal subgroup of | C2×#72221870 |
Past the SmallGroups library coverage — no SmallGroups id.