Finite Group DatabasebetaFinite Group Databasebeta| order | 30276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C29 |
| direct product | C22×C292⋊C9 |
| derived, Sylow | C292 ⋊ C22×C9 |
| Hall | C22×C292 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | C292⋊C3 |
| commutator, hypocenter | C292 | C22×C9 |
| Frattini | C3 | C22×C292⋊C3 |
| Fitting, socle, prime radical | C22×C3×C292 | C3 |
| cosocle | C3×C292 | C22×C3 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C22×C3 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1044 |
3396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30276, 67);