Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#11718246 |
| Fitting | C2×C13×C4⋊C4 ⋊ C4 |
| Sylow | C13 ⋊ C2×#340 |
512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#340, C4×#11718246, #16785212, … |
| maximal normal subgroup of | #261×#340, C4×#11718246, #16785212, … |
| maximal quotient of | C2×#13129665, #16779002, #16779012, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20193);