Finite Group DatabasebetaFinite Group Databasebeta| order | 14994 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C3 |
| direct product | C7×C3⋊D357 |
| unambiguous semidirect product | C3⋊(C7×D357) |
| unambiguous semidirect product | C7⋊(C7×C3⋊D51) |
| unambiguous semidirect product | C17⋊(C7×C3⋊D21) |
| Fitting, socle, Hall | C32×C72×C17 ⋊ C2 |
| derived | C32×C7×C17 ⋊ C2×C7 |
| Hall | C72×C17 ⋊ C3⋊D3 |
| Hall | C32×C72 ⋊ D17 |
| Hall | C32×C17 ⋊ C7×D7 |
| Sylow | C72 ⋊ C3⋊D51 |
| Sylow | C17 ⋊ C7×C3⋊D21 |
| Sylow | C32 ⋊ C7×D119 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊D357 |
| commutator, cosocle, hypocenter | C32×C7×C17 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C17 | C2 |
| LCS | G ▷ C32×C7×C17 | |
| UCS | C1 ◁ C7 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2142 |
3759 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×D357, C7×D21×D51, D21⋊D357, … |
| maximal normal subgroup of | D3×C7×D357, C7×D21×D51, D21⋊D357, … |
| maximal quotient of | C7×C3⋊Dic357, C2×C7×C3⋊D357 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14994, 122);