Finite Group DatabasebetaFinite Group Databasebeta| order | 30396 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C17×#10597010 |
| Fitting, socle, Hall | C3×C17×C149 ⋊ C4 |
| derived, Sylow | C149 ⋊ C3×C4×C17 |
| Hall | C17×C149 ⋊ C3×C4 |
| Hall | C3×C149 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | #10597010 |
| commutator, hypocenter | C149 | C3×C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C149 | C4 |
| prime radical | C3×C17×D149 | C2 |
| cosocle | D149 | C2×C3×C17 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C3×C17 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7599 |
2091 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30396, 10);