Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×#72210409 |
| Fitting, Sylow | C2×#72209716 ⋊ C3 |
| derived | #72209716 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72210409 |
| commutator, cosocle, hypocenter | #72209716 | C2×C3 |
| Frattini | C26 | C2×C22⋊A4 |
| Fitting | C2×#72209716 | C3 |
| socle | C23 | #11709313 |
| LCS | G ▷ #72209716 | |
| UCS | C1 ◁ C2 | |
At least 10725 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has at least 10725 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
92 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72210665 |
| maximal normal subgroup of | C2×#72210665 |
| automorphism group of | #383 |
Past the SmallGroups library coverage — no SmallGroups id.