Finite Group DatabasebetaFinite Group Databasebeta| order | 14994 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3×C7 |
| unambiguous semidirect product | C3⋊(C3⋊(C7⋊D119)) |
| unambiguous semidirect product | C7⋊(C3⋊D357) |
| unambiguous semidirect product | C17⋊(C3⋊(C3⋊(C7⋊D7))) |
| Fitting, socle, derived, Hall | C32×C72×C17 ⋊ C2 |
| 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, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C72×C17 | C2 |
| LCS | G ▷ C32×C72×C17 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7497 |
Polycyclic presentation:
2,3^2,7^2,17|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^6,f^a=f^163750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44472908, D21×D357, D3×C3⋊(C7⋊D119), … |
| maximal normal subgroup of | #44472908, D21×D357, D3×C3⋊(C7⋊D119), … |
| maximal quotient of | C3⋊(C3⋊(C7⋊Dic119)), C2×C3⋊(C3⋊(C7⋊D119)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14994, 120);