Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C7 |
| unambiguous semidirect product | C7⋊(C7⋊#10597479) |
| Fitting, socle, derived, Hall | C32×C72×C17 ⋊ C4 |
| Hall | C72×C17 ⋊ #157 |
| Hall | C32×C72 ⋊ #595 |
| Hall | C32×C17 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ #10597479 |
| Sylow | C17 ⋊ C7⋊(C7⋊#157) |
| Sylow | C32 ⋊ C7⋊(C7⋊#595) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C72×C17 | C4 |
| prime radical, cosocle | C72×C3⋊D51 | C2 |
| LCS | G ▷ C32×C72×C17 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4998 |
Polycyclic presentation:
2^2,3^2,7^2,17|a^2=b,c^a=cd,d^a=cd^2,e^a=e^6,f^a=f^6,g^a=g^13,c^b=c^2,d^b=d^2,g^b=g^161914 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 558);