Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #6095 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D104 |
| Fitting | C23×C8×C13 ⋊ C2 |
| Sylow | C13 ⋊ C23×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D52 |
| commutator, cosocle | C4×C13 | C25 |
| Frattini | C4 | C24×D13 |
| Fitting | C23×C8×C13 | C2 |
| socle | C24×C13 | D4 |
| hypercenter | C23×C8 | D13 |
| hypocenter | C13 | C23×D8 |
| LCS | G ▷ C4×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15769717, #15769719, #15769743, … |
| maximal normal subgroup of | #15769717, #15769719, #15769743, … |
| maximal quotient of | C23×#88061, C23×#88058, C22×C4×D104, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19226);