Finite Group DatabasebetaFinite Group Databasebeta| order | 26852 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×#10587739 |
| Fitting, Hall | C49×C137 ⋊ C4 |
| derived, Sylow | C137 ⋊ C4×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | #10587739 |
| commutator, hypocenter | C137 | C4×C49 |
| Frattini | C7 | C7×#10587739 |
| Fitting | C49×C137 | C4 |
| socle | C7×C137 | C4×C7 |
| prime radical, cosocle | C7×D137 | C2×C7 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C49 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6713 |
1862 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26852, 6);