Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #1445 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D13 |
| commutator | C23×C13 | C22×C4 |
| Fitting | C2×C13×#95 | C2 |
| socle, prime radical, cosocle | C24×C13 | C23 |
| hypercenter | C2×#95 | D13 |
| hypocenter | C13 | #1445 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=de,c^2=de,b^a=bd,c^a=ce,c^b=cf,h^c=h^12284 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1445, C2×#13113102, #15784642, … |
| maximal normal subgroup of | D13×#1445, C2×#13113102, #15784642, … |
| maximal quotient of | #15750843, #15750844, #15750845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2776);