Finite Group DatabasebetaFinite Group Databasebeta| order | 1352 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×C22⋊D13 |
| unambiguous semidirect product | C22⋊(C13×D13) |
| Fitting | C22×C132 ⋊ C2 |
| Sylow | C132 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C13 | C2×D13 |
| commutator, cosocle | C2×C13 | C22×C13 |
| Frattini | C2 | C2×C13×D13 |
| Fitting | C22×C132 | C2 |
| socle | C2×C132 | C22 |
| hypercenter | C22×C13 | D13 |
| hypocenter | C13 | D4×C13 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C13 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 52 |
377 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72214085, #72214115, C2×C13×C22⋊D13, … |
| maximal normal subgroup of | #72214085, #72214115, C2×C13×C22⋊D13, … |
| maximal quotient of | C2×C13×C22⋊D13, C13×#6105, C13×#6104 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1352, 31);