Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C42×Dic13 |
| derived, Sylow | C13 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D13 |
| commutator, hypocenter | C13 | C2×C43 |
| Frattini | C23 | C23×D13 |
| Fitting | C22×C42×C13 | C2 |
| socle, prime radical | C24×C13 | C23 |
| cosocle | C23×C13 | C24 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C42 | |
1272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13112668, #15752360, Dic13×#336, … |
| maximal normal subgroup of | C2×#13112668, #15752360, Dic13×#336, … |
| maximal quotient of | C43×Dic13, C2×#95×Dic13, C2×C4×#88071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6832);