Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C17 · Schur multiplier (H2) = C2×C3×C7 |
| direct product | A4×C17×#3862 |
| Fitting, socle, Hall | C22×C72×C17 ⋊ C32 |
| derived, Hall | C22×C72 ⋊ C32×C17 |
| Hall | C72×C17 ⋊ C3×A4 |
| Hall | C22×C17 ⋊ C3×#3862 |
| Sylow | C72 ⋊ C3×A4×C17 |
| Sylow | C22 ⋊ C3×C17×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | A4×#3862 |
| commutator, cosocle, hypocenter | C22×C72 | C32×C17 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C17 | C32 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 ◁ C17 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1428 |
1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 505);