Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C7 |
| unambiguous semidirect product | C3⋊#23756206 |
| Fitting, socle | C3×C72×C17 ⋊ Dic3 |
| derived, Hall | C3×C17×#3862 ⋊ C4 |
| Hall | C72×C17 ⋊ C3⋊Dic3 |
| Hall | C3×#3862 ⋊ #595 |
| Sylow | C72 ⋊ C3⋊(C3⋊#595) |
| Sylow | C17 ⋊ C3⋊#10596885 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×C17×#3862 | C4 |
| Fitting, socle | C3×C72×C17 | Dic3 |
| prime radical, cosocle | C3×C17⋊#64425 | C2 |
| LCS | G ▷ C3×C17×#3862 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 714 |
Polycyclic presentation:
2^2,3^2,17,7^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^13,f^a=f^5g^2,g^a=fg^2,e^b=e^16,f^b=f^6,g^b=g^6,f^c=f^4g^4,g^c=g^2252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 414);