Finite Group DatabasebetaFinite Group Databasebeta| order | 14994 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C17 · Schur multiplier (H2) = C7 |
| direct product | C17×#11725078 |
| derived, Sylow | C72 ⋊ C2×C9×C17 |
| Hall | C17×#89205 ⋊ C2 |
| Hall | C17×C7⋊D7 ⋊ C9 |
| Hall | C72×C17 ⋊ C2×C9 |
| Hall | #89205 ⋊ C2×C17 |
| Hall | C7⋊D7 ⋊ C9×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | #64425 |
| commutator, hypocenter | C72 | C2×C9×C17 |
| Frattini | C3 | C17×#64425 |
| Fitting, socle | C3×C72×C17 | C2×C3 |
| prime radical | C3×C17×C7⋊D7 | C3 |
| cosocle | C3×C72 | C2×C3×C17 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C17 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1071 |
714 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×#11725078, C17×#11725075⋊C2, #44472536, … |
| maximal normal subgroup of | D17×#11725078, C17×#11725075⋊C2, #44472536, … |
| maximal quotient of | C17×#13183534, C2×C17×#11725078 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14994, 39);