Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#11719537 |
| Fitting | C22×C13×#41 ⋊ C2 |
| Sylow | C13 ⋊ C2×#532 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D13 |
| commutator, cosocle | C22×C13 | C25 |
| Frattini | C22 | C24×D13 |
| Fitting | C22×C13×#41 | C2 |
| socle | C23×C13 | C24 |
| hypercenter | C22×#41 | D13 |
| hypocenter | C13 | C2×#532 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
1728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15769474, #15769475, #15769478, … |
| maximal normal subgroup of | #15769474, #15769475, #15769478, … |
| maximal quotient of | C2×#13117239, C2×#13117295, C2×#13117324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17789);