Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C11 |
| unambiguous semidirect product | C3⋊(C3⋊(C7⋊#92150)) |
| unambiguous semidirect product | C7⋊(C3⋊(C3⋊#92150)) |
| Fitting, socle, derived, Hall | C32×C7×C112 ⋊ C4 |
| Hall | C32×C112 ⋊ Dic7 |
| Hall | C7×C112 ⋊ C3⋊Dic3 |
| Sylow | C112 ⋊ C3⋊Dic21 |
| Hall | C32×C7 ⋊ #92150 |
| Sylow | C32 ⋊ C7⋊#92150 |
| Sylow | C7 ⋊ C3⋊(C3⋊#92150) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C112 | C4 |
| prime radical, cosocle | C32×C7×C11⋊D11 | C2 |
| LCS | G ▷ C32×C7×C112 | |
| UCS | C1 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1386 |
Polycyclic presentation:
2^2,3^2,7,11^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^6,f^a=f^8g^8,g^a=f^7g^3,f^b=f^10,g^b=g^101956 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 458);