Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C13×#386 ⋊ C2 |
| Sylow | C13 ⋊ #2709 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C13×#386 | C2 |
| prime radical | C2×#88194 | C2 |
| hypercenter | #386 | D13 |
| hypocenter | C13 | #2709 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #386 | |
612 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=e,c^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^c=h^12,h^d=h^12200 conjugacy classes — view the full character table.
| maximal subgroup of | #16070274, #16070276, #16070484, … |
| maximal normal subgroup of | #16070274, #16070276, #16070484, … |
| maximal quotient of | #15790463, #15790465, #15791009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 11238);