Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×D4×C22⋊D13 |
| Fitting | C23×D4×C13 ⋊ C2 |
| Sylow | C13 ⋊ C2×D42 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D13 |
| commutator, cosocle | C22×C13 | C25 |
| Frattini | C22 | C24×D13 |
| Fitting | C23×D4×C13 | C2 |
| socle | C23×C13 | C24 |
| hypercenter | C23×D4 | D13 |
| hypocenter | C13 | C2×D42 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
2536 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15754581, #15878237, D4×#88046, … |
| maximal normal subgroup of | #15754581, #15878237, D4×#88046, … |
| maximal quotient of | C2×D4×#6103, C2×C22⋊C4×C22⋊D13, C2×D4×C22⋊Dic13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17947);