Finite Group DatabasebetaFinite Group Databasebeta| order | 30084 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C23×#89137 |
| Fitting, socle, Hall | C3×C23×C109 ⋊ C4 |
| derived, Sylow | C109 ⋊ C3×C4×C23 |
| Hall | C23×C109 ⋊ C3×C4 |
| Hall | C3×C109 ⋊ C4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | #89137 |
| commutator, hypocenter | C109 | C3×C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C109 | C4 |
| prime radical | C3×C23×D109 | C2 |
| cosocle | D109 | C2×C3×C23 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C3×C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7521 |
2139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30084, 20);