Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C7 |
| unambiguous semidirect product | C3⋊(C3⋊(C7⋊(C7⋊#595))) |
| unambiguous semidirect product | C7⋊(C3⋊(C3⋊(C7⋊#595))) |
| Fitting, socle, derived, Hall | C32×C72×C17 ⋊ C4 |
| Hall | C72×C17 ⋊ C3⋊Dic3 |
| Hall | C32×C72 ⋊ #595 |
| Hall | C32×C17 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C3⋊(C3⋊#595) |
| Sylow | C17 ⋊ C3⋊(C3⋊(C7⋊Dic7)) |
| Sylow | C32 ⋊ C7⋊(C7⋊#595) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C72×C17 | C4 |
| prime radical, cosocle | C32×C72×D17 | C2 |
| LCS | G ▷ C32×C72×C17 | |
| UCS | C1 | |
360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7497 |
Polycyclic presentation:
2^2,3^2,7^2,17|a^2=b,c^a=c^2,d^a=d^2,e^a=e^6,f^a=f^6,g^a=g^13,g^b=g^162208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 637);