Finite Group DatabasebetaFinite Group Databasebeta| order | 24540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C5⋊(D409⋊C3) |
| unambiguous semidirect product | (C2×C5)⋊(D409⋊C3) |
| unambiguous semidirect product | (C2×C409⋊C3)⋊D5 |
| unambiguous semidirect product | (C2×D2045)⋊C3 |
| Fitting, socle | C2×C5×C409 ⋊ C2×C3 |
| derived, Hall | C5×C409 ⋊ C22×C3 |
| Hall | C2×D2045 ⋊ C3 |
| Hall | C5×C409⋊C3 ⋊ C22 |
| Hall | C409⋊C3 ⋊ C2×D5 |
| Sylow | C409 ⋊ C2×C3×D5 |
| Sylow | C5 ⋊ C2×D409⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊(D409⋊C3) |
| commutator, cosocle, hypocenter | C5×C409 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C409 | C2×C3 |
| LCS | G ▷ C5×C409 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4090 |
704 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24540, 22);