Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C42 |
| direct product | C2×#11709340 |
| Fitting, Sylow | C2×#17309 ⋊ C3 |
| derived | #17309 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #5464 |
| commutator, cosocle, hypocenter | #17309 | C2×C3 |
| Frattini | C24 | C2×C22⋊A4 |
| Fitting | C2×#17309 | C3 |
| socle | C25 | C22⋊A4 |
| LCS | G ▷ #17309 | |
| UCS | C1 ◁ C23 | |
1827 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 1827 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
52 conjugacy classes — view the full character table.
| maximal subgroup of | #72210078, #72210080, #72210085, … |
| maximal normal subgroup of | #72210085, C2×#72209705, C22×#11709340, … |
| maximal quotient of | C22×#11709340, #72266643 |
Past the SmallGroups library coverage — no SmallGroups id.