Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#828 |
| Fitting | C22×C3×Q16 ⋊ C2 |
| Sylow | C3 ⋊ C22×SD32 |
400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 149 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 — 4 generators on 23 points:
(5,6,7)(8,9,12,15)(10,17,19,23)(11,20,18,14)(13,21,22,16);(6,7)(9,13)(10,16)(11,18)(14,23)(15,22)(17,20)(19,21);(3,4);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10712249, #10712251, #10712255, … |
| maximal normal subgroup of | #10712249, #10712251, #10712255, … |
| maximal quotient of | C22×#4491, C22×#4564, C22×#4490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16445);