Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D4×#6103 |
| Fitting | C2×C4×D4×C13 ⋊ C2 |
| Sylow | C13 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15878624, #15878625, #15878632, … |
| maximal normal subgroup of | #15878624, #15878625, #15878632, … |
| maximal quotient of | C22⋊C4×#6103, C4⋊C4×#6103, D4×#88071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7327);