Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| unambiguous semidirect product | D51⋊(C3⋊(C7⋊D7)) |
| Fitting, socle, derived, Hall | C32×C72×C17 ⋊ C22 |
| Hall | C72×C17 ⋊ D32 |
| Hall | C32×C72 ⋊ C2×D17 |
| Hall | C32×C17 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ (C3⋊D3)⋊D17 |
| Sylow | C17 ⋊ D3×C3⋊(C7⋊D7) |
| Sylow | C32 ⋊ D17×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C72×C17 | C22 |
| LCS | G ▷ C32×C72×C17 | |
| UCS | C1 | |
440 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4998 |
Polycyclic presentation:
2^2,3^2,7^2,17|d^a=d^2,g^a=g^16,c^b=c^2,d^b=d^2,e^b=e^6,f^b=f^62001 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 614);