Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D5×C31×D49 |
| unambiguous semidirect product | (D5×C49)⋊(C2×C31) |
| unambiguous semidirect product | (C5×D49)⋊(C2×C31) |
| unambiguous semidirect product | D245⋊(C2×C31) |
| Fitting, Hall | C5×C31×C49 ⋊ C22 |
| derived, Hall | C5×C49 ⋊ C22×C31 |
| Hall | C31×C49 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×D5×C31 |
| Sylow | C5 ⋊ C2×C31×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D5×D49 |
| commutator, cosocle, hypocenter | C5×C49 | C22×C31 |
| Frattini | C7 | D5×D7×C31 |
| Fitting | C5×C31×C49 | C22 |
| socle | C5×C7×C31 | C2×D7 |
| LCS | G ▷ C5×C49 | |
| UCS | C1 ◁ C31 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7595 |
3224 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 26);