Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×#1055 |
| derived, Sylow | C13 ⋊ C22×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D13 |
| commutator, hypocenter | C13 | C22×C4×C8 |
| Frattini | C2×C4 | C23×D13 |
| Fitting | C22×C42×C13 | C2 |
| socle, prime radical | C24×C13 | C2×C4 |
| cosocle | C2×C4×C13 | C24 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C42 | |
760 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13112663, #15752300, #15752302, … |
| maximal normal subgroup of | C2×#13112663, #15752300, #15752302, … |
| maximal quotient of | C22×C8×#1055, C22×#11718047, C2×M16×#1055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12911);