Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×D4×C13 ⋊ C4 |
| Sylow | C13 ⋊ #2349 |
704 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=g,c^2=ef,b^a=be,c^a=cf,h^a=h^8,d^b=de,h^g=h^12110 conjugacy classes — view the full character table.
| maximal subgroup of | #16783391, #16783392, #16783399, … |
| maximal normal subgroup of | #16783391, #16783392, #16783399, … |
| maximal quotient of | #16791622, #16791627, D4×(C2×#261)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21023);