Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #6118 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4⋊#261 |
| unambiguous semidirect product | D13⋊(C22×C4⋊C4) |
| Fitting | C23×C4×C13 ⋊ C4 |
| Sylow | C13 ⋊ C23×C4⋊C4 |
2488 conjugacy classes of subgroups; only the 1106 normal subgroups are shown.
This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #16778230, #16785294, #16785306, … |
| maximal normal subgroup of | #16778230, #16785294, #16785306, … |
| maximal quotient of | C23×(C2×#261)⋊C4, C22×C4×C4⋊#261, C22×#11719136, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21482);