Finite Group DatabasebetaFinite Group Databasebeta| order | 21725 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C79 · Schur multiplier (H2) = C5 |
| Fitting, socle | C5×C11×C79 ⋊ C5 |
| derived, Sylow | C11 ⋊ C52×C79 |
| Hall | C11×C79 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C79 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C52×C79 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C79 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C5×C79 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4345 |
2765 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21725, 4);