Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #1436 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D13 |
| commutator | C22×C13 | C2×C42 |
| Fitting | C2×C13×#95 | C2 |
| socle, prime radical, cosocle | C24×C13 | C23 |
| hypercenter | C2×#95 | D13 |
| hypocenter | C13 | #1436 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
612 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=g,c^2=f,b^a=bd,c^a=ce,h^a=h^12,h^b=h^12296 conjugacy classes — view the full character table.
| maximal subgroup of | #15754433, D13×#1436, C2×#13113071, … |
| maximal normal subgroup of | #15754433, D13×#1436, C2×#13113071, … |
| maximal quotient of | #15750838, #15750842, #15750845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2745);