Finite Group DatabasebetaFinite Group Databasebeta| order | 21316 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×#64408 |
| Fitting, socle, Sylow | C732 ⋊ C4 |
| derived | C73 ⋊ C4×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | #64408 |
| commutator, hypocenter | C73 | C4×C73 |
| Frattini | C1 | G |
| Fitting, socle | C732 | C4 |
| prime radical | C73×D73 | C2 |
| cosocle | D73 | C2×C73 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C73 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 292 |
1606 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21316, 10);