Finite Group DatabasebetaFinite Group Databasebeta| order | 30276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C29 |
| unambiguous semidirect product | (C3⋊D3)⋊(C29⋊D29) |
| Fitting, socle, derived, Hall | C32×C292 ⋊ C22 |
| Sylow | C292 ⋊ D32 |
| Sylow | C32 ⋊ C2×C29⋊D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C292 | C22 |
| LCS | G ▷ C32×C292 | |
| UCS | C1 | |
704 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5046 |
Polycyclic presentation:
2^2,3^2,29^2|d^a=d^2,e^a=e^28,f^a=f^28,c^b=c^2,d^b=d^22529 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30276, 130);