Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| unambiguous semidirect product | D153⋊(C7⋊D7) |
| Fitting, derived, Hall | C72×C9×C17 ⋊ C22 |
| Hall | C72×C17 ⋊ C2×D9 |
| Hall | C72×C9 ⋊ C2×D17 |
| Hall | C9×C17 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ D9×D17 |
| Sylow | C17 ⋊ D9×C7⋊D7 |
| Sylow | C9 ⋊ D17×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C72×C9×C17 | C22 |
| Frattini | C3 | D51⋊(C7⋊D7) |
| socle | C3×C72×C17 | C2×D3 |
| LCS | G ▷ C72×C9×C17 | |
| UCS | C1 | |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7497 |
Polycyclic presentation:
2^2,3,7^2,17,3|c^3=g^2,d^a=d^6,e^a=e^6,f^a=f^16,c^b=c^2g,d^b=d^6,e^b=e^6,g^b=g^21932 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 246);