Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C82×C13 ⋊ C2 |
| Sylow | C13 ⋊ #1454 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D13 |
| commutator, socle | C22×C13 | C2×C42 |
| Fitting | C82×C13 | C2 |
| prime radical | C22×D13 | C42 |
| cosocle | C42×C13 | C23 |
| hypercenter | C82 | D13 |
| hypocenter | C13 | #1454 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C42 ◁ C82 | |
178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cfg,c^b=cf,h^c=h^12440 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1454, C2×#13113135, #15828551, … |
| maximal normal subgroup of | D13×#1454, C2×#13113135, #15828551, … |
| maximal quotient of | #15752291, #15752309, #15753353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2809);