Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×#72209720 |
| Fitting, Sylow | C2×#72209716 ⋊ C3 |
| derived | #62817 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23 | #11709314 |
| commutator, cosocle, hypocenter | #62817 | C23×C3 |
| Frattini | C26 | C23×A4 |
| Fitting | C2×#72209716 | C3 |
| LCS | G ▷ #62817 | |
| UCS | C1 ◁ C23 | |
719508 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 719508 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 32 |
156 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.