Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C13×#125 ⋊ C2 |
| Sylow | C13 ⋊ #3563 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D13 |
| commutator, socle, cosocle | C22×C13 | C25 |
| Fitting | C2×C13×#125 | C2 |
| prime radical | #88184 | C22 |
| hypercenter | C2×#125 | D13 |
| hypocenter | C13 | #3563 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C2×#125 | |
912 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=f,c^2=f,d^2=g,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^12,c^b=cg,d^b=df206 conjugacy classes — view the full character table.
| maximal subgroup of | #15755230, #15755234, #15755391, … |
| maximal normal subgroup of | #15755230, #15755234, #15755391, … |
| maximal quotient of | #16025874, #16025930, #16026177, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19116);