Finite Group DatabasebetaFinite Group Databasebeta| order | 26852 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C137 · Schur multiplier (H2) = C1 |
| direct product | C137×Dic49 |
| unambiguous semidirect product | C49⋊(C4×C137) |
| derived, Sylow | C49 ⋊ C4×C137 |
| Hall | C49×C137 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C137 | D49 |
| commutator, hypocenter | C49 | C4×C137 |
| Frattini | C2×C7 | D7×C137 |
| Fitting | C2×C49×C137 | C2 |
| socle, prime radical | C2×C7×C137 | D7 |
| cosocle | C2×C49 | C2×C137 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C137 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26852 |
7124 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26852, 2);