Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C11 |
| unambiguous semidirect product | C7⋊(C11⋊(C11⋊#157)) |
| unambiguous semidirect product | C11⋊(C7⋊(C11⋊#157)) |
| Fitting, socle, derived, Hall | C32×C7×C112 ⋊ C4 |
| Hall | C32×C112 ⋊ Dic7 |
| Hall | C7×C112 ⋊ #157 |
| Sylow | C112 ⋊ C7⋊#157 |
| Hall | C32×C7 ⋊ C11⋊Dic11 |
| Sylow | C32 ⋊ C7⋊(C11⋊Dic11) |
| Sylow | C7 ⋊ C11⋊(C11⋊#157) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C112 | C4 |
| prime radical, cosocle | C7×C112×C3⋊D3 | C2 |
| LCS | G ▷ C32×C7×C112 | |
| UCS | C1 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5082 |
Polycyclic presentation:
2^2,3^2,7,11^2|a^2=b,c^a=cd,d^a=cd^2,e^a=e^6,f^a=f^10,g^a=g^10,c^b=c^2,d^b=d^22544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 401);