Finite Group DatabasebetaFinite Group Databasebeta| order | 14994 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C17 · Schur multiplier (H2) = C3 |
| direct product | C32×C17×D49 |
| Fitting, Hall | C32×C17×C49 ⋊ C2 |
| derived, Sylow | C49 ⋊ C2×C32×C17 |
| Hall | C17×C49 ⋊ C2×C32 |
| Hall | C32×C49 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C17 | D49 |
| commutator, cosocle, hypocenter | C49 | C2×C32×C17 |
| Frattini | C7 | C32×D7×C17 |
| Fitting | C32×C17×C49 | C2 |
| socle | C32×C7×C17 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C32×C17 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7497 |
3978 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D17×D49, C3×D3×C17×D49, C3×D49×D51, … |
| maximal normal subgroup of | C32×D17×D49, C3×D3×C17×D49, C3×D49×D51, … |
| maximal quotient of | C32×C17×Dic49, C2×C32×C17×D49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14994, 23);