Finite Group DatabasebetaFinite Group Databasebeta| order | 22740 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×(C379⋊C3)⋊C4 |
| unambiguous semidirect product | (C379⋊C3)⋊(C4×C5) |
| unambiguous semidirect product | Dic379⋊(C3×C5) |
| unambiguous semidirect product | (C5×Dic379)⋊C3 |
| derived, Sylow | C379 ⋊ C3×C4×C5 |
| Hall | C5×Dic379 ⋊ C3 |
| Hall | C5×C379⋊C3 ⋊ C4 |
| Hall | C5×C379 ⋊ C3×C4 |
| Hall | Dic379 ⋊ C3×C5 |
| Hall | C379⋊C3 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D379⋊C3 |
| commutator, hypocenter | C379 | C3×C4×C5 |
| Frattini | C2 | C5×D379⋊C3 |
| Fitting, socle | C2×C5×C379 | C2×C3 |
| prime radical | C2×C5×C379⋊C3 | C2 |
| cosocle | C2×C379 | C2×C3×C5 |
| LCS | G ▷ C379 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7580 |
690 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22740, 10);