Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#883 |
| Fitting | C22×C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C22×#123 |
1968 conjugacy classes of subgroups; only the 605 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 605 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 5 generators on 19 points:
(1,2)(3,4)(5,6,7)(8,9)(10,11)(12,14)(13,17)(15,19)(16,18);(1,2)(3,4)(9,11)(12,14,15,19)(13,16,18,17);(6,7)(12,13)(14,16)(15,18)(17,19);(3,4);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10686532, #10687796, #10687827, … |
| maximal normal subgroup of | #10686532, #10687796, #10687827, … |
| maximal quotient of | C22×#4664, C22×#4668, C22×#4956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18269);