Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D13×#400 |
| Fitting | C13×#400 ⋊ C2 |
| Sylow | C13 ⋊ C2×#400 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C13×#400 | C2 |
| prime radical | C23×D13 | C23 |
| hypercenter | #400 | D13 |
| hypocenter | C13 | C2×#400 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #400 | |
604 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1353, #15773651, D13×#1615, … |
| maximal normal subgroup of | D13×#1353, #15773651, D13×#1615, … |
| maximal quotient of | D13×#1441, D13×#1442, D13×#1443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7760);