Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C13×#131 ⋊ C4 |
| Sylow | C13 ⋊ #2875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#261 |
| commutator, socle | C2×C13 | C22×C42 |
| Fitting | C13×#131 | C4 |
| prime radical | #41×D13 | C22 |
| cosocle | C4×D13 | C24 |
| hypercenter | #131 | #261 |
| hypocenter | C13 | #2875 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C4 ◁ #131 | |
556 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=f,e^2=g,b^a=bg,h^b=h^8,d^c=dg,h^f=h^12128 conjugacy classes — view the full character table.
| maximal subgroup of | #16789344, #16789345, #16797434, … |
| maximal normal subgroup of | #16789344, #16789345, #16797434, … |
| maximal quotient of | #16792593, #16792594, #16792595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21080);