Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#11719420 |
| Fitting | C2×C13×#127 ⋊ C2 |
| Sylow | C13 ⋊ C2×#535 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D13 |
| commutator, cosocle | C22×C13 | C25 |
| Frattini | C22 | C24×D13 |
| Fitting | C2×C13×#127 | C2 |
| socle | C23×C13 | C24 |
| hypercenter | C2×#127 | D13 |
| hypocenter | C13 | C2×#535 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
1896 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | #15755438, #15778413, #15778417, … |
| maximal normal subgroup of | #15755438, #15778413, #15778417, … |
| maximal quotient of | C2×#13117415, C2×#13117426, C2×#13117457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17815);