Finite Group DatabasebetaFinite Group Databasebeta| order | 5832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#72221848 |
| Fitting | C2×#10624918 ⋊ C22 |
| derived | #6903 ⋊ C23×C3 |
| Sylow | #10624918 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72221848 |
| commutator, cosocle, hypocenter | #6903 | C23×C3 |
| Frattini | C9 | C2×C3×#1113 |
| Fitting | C2×#10624918 | C22 |
| socle | C2×C3 | C3×#66431 |
| LCS | G ▷ #6903 | |
| UCS | C1 ◁ C2 | |
904 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 904 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221857, C2×#72221860 |
| maximal normal subgroup of | C2×#72221860 |
Past the SmallGroups library coverage — no SmallGroups id.