Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C13×#399 ⋊ C2 |
| Sylow | C13 ⋊ #2780 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C13×#399 | C2 |
| prime radical | C22×C22⋊D13 | C22 |
| hypercenter | #399 | D13 |
| hypocenter | C13 | #2780 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #399 | |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=efg,b^2=e,d^2=ef,b^a=be,c^a=cf,d^a=def,h^a=h^12,c^b=cg,d^b=de,h^b=h^12,h^d=h^12164 conjugacy classes — view the full character table.
| maximal subgroup of | #16070509, #16070510, #16070517, … |
| maximal normal subgroup of | #16070509, #16070510, #16070517, … |
| maximal quotient of | #15790713, #15790920, #15791313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12163);