Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C26×D13 |
| unambiguous semidirect product | C13⋊C27 |
| unambiguous semidirect product | (C2×C13)⋊C26 |
| Fitting, socle | C26×C13 ⋊ C2 |
| derived, Sylow | C13 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26 | D13 |
| commutator, cosocle, hypocenter | C13 | C27 |
| Frattini | C1 | G |
| Fitting, socle | C26×C13 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C26 | |
58424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15794074, C2×D13×#379, C22×#11718616, … |
| maximal normal subgroup of | #15794074, C2×D13×#379, C22×#11718616, … |
| maximal quotient of | C25×C4×D13, C26×Dic13, C24×D4×D13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19324);