Finite Group DatabasebetaFinite Group Databasebeta| order | 14994 |
| isoclinism | isoclinic class of C49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C17 · Schur multiplier (H2) = C3 |
| Fitting | C2×C3×C17×C49 ⋊ C3 |
| derived, Sylow | C49 ⋊ C2×C32×C17 |
| Hall | C2×C17×C49 ⋊ C32 |
| Hall | C17×C49 ⋊ C2×C32 |
| Hall | C2×C49 ⋊ C32×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C17 | C49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C2×C32×C17 |
| Frattini | C7 | C2×C3×C17×ΓL(1,𝔽8) |
| Fitting | C2×C3×C17×C49 | C3 |
| socle | C2×C3×C7×C17 | ΓL(1,𝔽8) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C3×C17 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4998 |
1938 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14994, 21);