Finite Group DatabasebetaFinite Group Databasebeta| order | 30276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#29502829 |
| derived, Hall | C292⋊C9 ⋊ C22 |
| Sylow | C292 ⋊ C2×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #29502829 |
| commutator, cosocle, hypocenter | C292⋊C9 | C22 |
| Frattini | C3 | C2×#19097943 |
| Fitting, socle | C2×C3×C292 | D3 |
| LCS | G ▷ C292⋊C9 | |
| UCS | C1 ◁ C2 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 522 |
936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30276, 50);