Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×(C2×#261)⋊C8 |
| Fitting | C22×C8×C13 ⋊ C4 |
| Sylow | C13 ⋊ C2×#336 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #16777232, #16777235, #261×#336, … |
| maximal normal subgroup of | #16777232, #16777235, #261×#336, … |
| maximal quotient of | C2×#13129658, D13⋊#1273, #16778892, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20169);