Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| direct product | ΓL(1,𝔽8)×C3⋊#92150 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)×#92150) |
| Fitting, socle, derived | C3×C7×C112 ⋊ C3×C4 |
| Hall | C3×C112×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C7×C112 ⋊ C3×Dic3 |
| Sylow | C112 ⋊ Dic3×ΓL(1,𝔽8) |
| Hall | C3×ΓL(1,𝔽8) ⋊ #92150 |
| Sylow | C7 ⋊ C3×C3⋊#92150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C112 | C3×C4 |
| prime radical | C3×ΓL(1,𝔽8)×C11⋊D11 | C2 |
| cosocle | C3×C7×C11⋊D11 | C2×C3 |
| LCS | G ▷ C3×C7×C112 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 462 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 335);