Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×C17⋊#64422 |
| unambiguous semidirect product | (C2×C17)⋊(C3×#64422) |
| Fitting, socle | C2×C3×C72×C17 ⋊ C2×C3 |
| derived, Hall | C72×C17 ⋊ C22×C32 |
| Hall | C3×C17×#3862 ⋊ C22 |
| Hall | C2×C7×D119 ⋊ C32 |
| Hall | C3×#3862 ⋊ C2×D17 |
| Sylow | C72 ⋊ C2×C32×D17 |
| Sylow | C17 ⋊ C2×C3×#64422 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C17⋊#64422 |
| commutator, cosocle, hypocenter | C72×C17 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C72×C17 | C2×C3 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C2×C3 | |
248 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4284 |
1014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 522);