Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #6104 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×#6106 |
| Fitting | C23×Q8×C13 ⋊ C2 |
| Sylow | C13 ⋊ C23×SD16 |
1720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15769720, #15769724, #15769747, … |
| maximal normal subgroup of | #15769720, #15769724, #15769747, … |
| maximal quotient of | C23×#88049, C23×#88075, C23×#88048, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19228);