Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C2×#11718037 |
| derived, Sylow | C13 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #261 |
| commutator, hypocenter | C13 | C2×C64 |
| Frattini | C16 | C2×#261 |
| Fitting | C2×C13×C16 | C4 |
| socle, prime radical | C22×C13 | C32 |
| cosocle | #88034 | C22 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C16 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11718037, #16778137, #16778139, … |
| maximal normal subgroup of | C4×#11718037, #16778137, #16778139, … |
| maximal quotient of | C4×#11718037, C22⋊#11718037, C4⋊#11718037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19677);