Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#11719335 |
| Fitting | C2×C13×C22⋊Q8 ⋊ C2 |
| Sylow | C13 ⋊ C2×#546 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D13 |
| commutator, cosocle | C22×C13 | C25 |
| Frattini | C22 | C24×D13 |
| Fitting | C2×C13×C22⋊Q8 | C2 |
| socle | C23×C13 | C24 |
| hypercenter | C2×C22⋊Q8 | D13 |
| hypocenter | C13 | C2×#546 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
1900 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
218 conjugacy classes — view the full character table.
| maximal subgroup of | #15754609, #15878277, #15878334, … |
| maximal normal subgroup of | #15754609, #15878277, #15878334, … |
| maximal quotient of | C2×#13117656, C2×#13117665, C2×#13117683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17956);