Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C4×#88147 |
| Fitting | C4×C13×C4⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ C42×D4 |
924 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15753510, #15753520, #15753530, … |
| maximal normal subgroup of | #15753510, #15753520, #15753530, … |
| maximal quotient of | C4×#11718327, C4×C4⋊C4×Dic13, #15784065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6855);