Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#950 |
| Fitting | C22×C3×#41 ⋊ C2 |
| Sylow | C3 ⋊ C22×#135 |
1504 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 565 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:
(5,6,7)(9,14)(11,19)(13,20)(15,16)(17,23)(21,22);(1,2)(3,4)(8,10,12,18)(9,13,16,22)(11,17,19,23)(14,20,15,21);(6,7)(8,9)(10,13)(11,14)(12,16)(15,19)(17,20)(18,22)(21,23);(3,4);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10702000, #10702001, #10702005, … |
| maximal normal subgroup of | #10702000, #10702001, #10702005, … |
| maximal quotient of | C22×#5002, C22×#5233, C22×#4998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19830);