Finite Group DatabasebetaFinite Group Databasebeta| order | 30849 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C113 · Schur multiplier (H2) = C1 |
| direct product | C113×#63270 |
| Fitting, socle, Hall | C7×C13×C113 ⋊ C3 |
| derived, Hall | C7×C13 ⋊ C3×C113 |
| Hall | C13×C113 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C113 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ ΓL(1,𝔽8)×C113 |
| Sylow | C7 ⋊ C13⋊C3×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C113 | #63270 |
| commutator, cosocle, hypocenter | C7×C13 | C3×C113 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C113 | C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C113 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10283 |
3729 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30849, 5);