Finite Group DatabasebetaFinite Group Databasebeta| order | 24353 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C49 · Schur multiplier (H2) = C7 |
| direct product | C49×C71⋊C7 |
| Fitting | C49×C71 ⋊ C7 |
| derived, Sylow | C71 ⋊ C7×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | C71⋊C7 |
| commutator, hypocenter | C71 | C7×C49 |
| Frattini | C7 | C7×C71⋊C7 |
| Fitting | C49×C71 | C7 |
| socle, cosocle | C7×C71 | C72 |
| prime radical | C7×C71⋊C7 | C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C49 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3479 |
833 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24353, 7);