Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #2594 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C13×#397 | C2 |
| prime radical | C24×C13 | C23 |
| hypercenter | #397 | D13 |
| hypocenter | C13 | #2594 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #397 | |
398 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=efg,c^2=g,d^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^12,c^b=cg,h^c=h^12,h^d=h^12170 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2594, C2×#13120345, #16033537, … |
| maximal normal subgroup of | D13×#2594, C2×#13120345, #16033537, … |
| maximal quotient of | #15785390, #15785559, #15786454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 10019);