Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊Dic119 |
| derived, Hall | C72×C17 ⋊ C4×C9 |
| Hall | C7×C17×C7⋊C9 ⋊ C4 |
| Hall | C7⋊Dic119 ⋊ C9 |
| Hall | C7×C7⋊C9 ⋊ Dic17 |
| Sylow | C72 ⋊ C9×Dic17 |
| Sylow | C17 ⋊ (C7⋊C9)⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C17⋊(ΓL(1,𝔽8)⋊D7) |
| commutator, hypocenter | C72×C17 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C72×C17 | C2×C3 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C2×C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4284 |
Polycyclic presentation:
2,3,7^2,17,2,3|a^2=f,b^3=g,c^a=c^6,d^a=d^6,e^a=e^16,c^b=c^21812 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 143);