Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×D4×C13 ⋊ C4 |
| Sylow | C13 ⋊ #2354 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=f,c^2=f,d^2=e,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 | #16782594, #16782598, #16782602, … |
| maximal normal subgroup of | #16782594, #16782598, #16782602, … |
| maximal quotient of | #16791618, C4⋊C4×C4⋊#261, #16791638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21028);