Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#916 |
| Fitting | C22×C3×SD16 ⋊ C2 |
| Sylow | C3 ⋊ C22×#135 |
1504 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 525 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 5 generators on 23 points:
(1,2)(3,4)(5,6,7)(8,10,12,18)(9,14,13,16)(11,20,19,17)(15,22,21,23);(1,2)(3,4)(9,13)(10,17)(11,19)(14,22)(16,23)(18,20);(6,7)(8,9)(10,16)(11,15)(12,13)(14,18)(17,22)(19,21)(20,23);(3,4);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10796531, #10796537, #10796646, … |
| maximal normal subgroup of | #10796531, #10796537, #10796646, … |
| maximal quotient of | C22×#4772, C22×#4804, C22×#4860, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19750);