Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C3⋊#23779029 |
| Fitting, socle, derived | C3×C7×C112 ⋊ C3×C4 |
| Hall | C3×C7×C112⋊C3 ⋊ C4 |
| Hall | C3×C112⋊C3 ⋊ Dic7 |
| Hall | C7×C112 ⋊ C3×Dic3 |
| Sylow | C112 ⋊ C3×Dic21 |
| Sylow | C7 ⋊ C3⋊(#92150⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C112 | C3×C4 |
| prime radical | C3×C7×(C11⋊D11)⋊C3 | C2 |
| cosocle | C3×C7×C11⋊D11 | C2×C3 |
| LCS | G ▷ C3×C7×C112 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1386 |
Polycyclic presentation:
2,3,2,3,7,11^2|a^2=c,d^a=d^2,e^a=e^6,f^a=f^5g^7,g^a=fg^6,f^b=f^9g^10,g^b=f^3g,f^c=f^10,g^c=g^10282 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 345);