Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C4×#88034 |
| derived, Sylow | C13 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D13 |
| commutator, hypocenter | C13 | C4×C32 |
| Frattini | C2×C16 | C2×D13 |
| Fitting | C4×C13×C16 | C2 |
| socle, prime radical | C22×C13 | C2×C16 |
| cosocle | C2×C13×C16 | C22 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C4×C16 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×#1055, C8×#88034, #15750246, … |
| maximal normal subgroup of | C32×#1055, C8×#88034, #15750246, … |
| maximal quotient of | C8×#88034, #15750250, #15750606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2642);