Finite Group DatabasebetaFinite Group Databasebeta| order | 28060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic61⋊C5 |
| unambiguous semidirect product | Dic61⋊(C5×C23) |
| unambiguous semidirect product | (C23×Dic61)⋊C5 |
| derived, Sylow | C61 ⋊ C4×C5×C23 |
| Hall | C23×C61⋊C5 ⋊ C4 |
| Hall | C23×Dic61 ⋊ C5 |
| Hall | C23×C61 ⋊ C4×C5 |
| Hall | C61⋊C5 ⋊ C4×C23 |
| Hall | Dic61 ⋊ C5×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D61⋊C5 |
| commutator, hypocenter | C61 | C4×C5×C23 |
| Frattini | C2 | C23×D61⋊C5 |
| Fitting, socle | C2×C23×C61 | C2×C5 |
| prime radical | C2×C23×C61⋊C5 | C2 |
| cosocle | C2×C61 | C2×C5×C23 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5612 |
736 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28060, 10);