Finite Group DatabasebetaFinite Group Databasebeta| order | 5616 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C22×C33 |
| direct product | A42×C13⋊C3 |
| Fitting, socle, derived, Hall | C24×C13 ⋊ C33 |
| Sylow | C24 ⋊ C32×C13⋊C3 |
| Sylow | C13 ⋊ C3×A42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C24×C13 | C33 |
| LCS | G ▷ C24×C13 | |
| UCS | C1 | |
316 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 156 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | A42×D13⋊C3, C13⋊C3×A4⋊S4, #72242077 |
| maximal normal subgroup of | A42×D13⋊C3, C13⋊C3×A4⋊S4, #72242077 |
Past the SmallGroups library coverage — no SmallGroups id.