Finite Group DatabasebetaFinite Group Databasebeta| order | 21550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×D431⋊C5 |
| unambiguous semidirect product | D431⋊C52 |
| unambiguous semidirect product | (C431⋊C5)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D431)⋊C5 |
| Fitting, socle | C5×C431 ⋊ C2×C5 |
| derived, Sylow | C431 ⋊ C2×C52 |
| Hall | C5×C431⋊C5 ⋊ C2 |
| Hall | D431 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D431⋊C5 |
| commutator, cosocle, hypocenter | C431 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C431 | C2×C5 |
| LCS | G ▷ C431 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2155 |
265 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21550, 8);