Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#14558785 |
| derived, Hall | C7×C19 ⋊ C22×C9 |
| Hall | #11924777 ⋊ C22 |
| Hall | C2×D7×C19 ⋊ C9 |
| Hall | C2×D7 ⋊ #4294 |
| Sylow | C19 ⋊ C2×D7⋊C9 |
| Sylow | C7 ⋊ C22×#4294 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2394 |
222 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#14558785, C2×C5×#14558785, C2×C5⋊#14558785, … |
| maximal normal subgroup of | C2×C5×#14558785, C2×C7×#14558785 |
| maximal quotient of | D5×#14558785, C2×C5×#14558785, C2×C5⋊#14558785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 39);