Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C13×#386 ⋊ C2 |
| Sylow | C13 ⋊ C4×#120 |
1224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=g,d^2=g,b^a=be,c^a=cf,h^a=h^12,h^c=h^12,h^d=h^12224 conjugacy classes — view the full character table.
| maximal subgroup of | #15778050, #15778881, #15868898, … |
| maximal normal subgroup of | #15778050, #15778881, #15868898, … |
| maximal quotient of | Dic13×#386, #15784070, #15784083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7015);