Finite Group DatabasebetaFinite Group Databasebeta| order | 30276 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C29 |
| unambiguous semidirect product | C3⋊(C3⋊#16809858) |
| Fitting, socle, derived, Hall | C32×C292 ⋊ C4 |
| Sylow | C292 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ #16809858 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C292 | C4 |
| prime radical, cosocle | C32×C29⋊D29 | C2 |
| LCS | G ▷ C32×C292 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 522 |
Polycyclic presentation:
2^2,3^2,29^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^17,f^a=f^12,e^b=e^28,f^b=f^281902 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30276, 137);