Finite Group DatabasebetaFinite Group Databasebeta| order | 26852 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C49⋊#10587739 |
| Fitting, derived, Hall | C49×C137 ⋊ C4 |
| Sylow | C137 ⋊ Dic49 |
| Sylow | C49 ⋊ #10587739 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C49×C137 | C4 |
| Frattini | C7 | C7⋊#10587739 |
| socle | C7×C137 | Dic7 |
| prime radical | C7×D137 | D7 |
| cosocle | C49×D137 | C2 |
| LCS | G ▷ C49×C137 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6713 |
Polycyclic presentation:
2^2,7,137,7|a^2=b,c^7=e^6,c^a=c^6e,d^a=d^100,e^a=e^6,d^b=d^1361718 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26852, 7);