Finite Group DatabasebetaFinite Group Databasebeta| order | 14994 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C7 |
| direct product | C3×C3⋊(C7⋊D119) |
| unambiguous semidirect product | C3⋊(C3×C7⋊D119) |
| unambiguous semidirect product | C17⋊(C3×C3⋊(C7⋊D7)) |
| Fitting, socle, Hall | C32×C72×C17 ⋊ C2 |
| derived | C3×C72×C17 ⋊ C2×C3 |
| Hall | C72×C17 ⋊ C3×D3 |
| Hall | C32×C72 ⋊ D17 |
| Hall | C32×C17 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C3×D51 |
| Sylow | C17 ⋊ C3×C3⋊(C7⋊D7) |
| Sylow | C32 ⋊ C7⋊D119 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C7⋊D119) |
| commutator, cosocle, hypocenter | C3×C72×C17 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C17 | C2 |
| LCS | G ▷ C3×C72×C17 | |
| UCS | C1 ◁ C3 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4998 |
3753 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D7×D357, C3×D21×D119, C3×D17×C3⋊(C7⋊D7), … |
| maximal normal subgroup of | C3×D7×D357, C3×D21×D119, C3×D17×C3⋊(C7⋊D7), … |
| maximal quotient of | C3×C3⋊(C7⋊Dic119), C2×C3×C3⋊(C7⋊D119) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14994, 126);