Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#915 |
| Fitting | C22×C3×SD16 ⋊ C2 |
| Sylow | C3 ⋊ C22×#137 |
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 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)(9,14)(10,16)(11,19)(13,20)(17,18)(21,23);(1,2)(3,4)(8,10,12,18)(9,13,14,21)(11,16,19,17)(15,23,22,20);(6,7)(8,9)(10,13)(11,15)(12,14)(16,23)(17,20)(18,21)(19,22);(3,4);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10796554, #10796560, #10796590, … |
| maximal normal subgroup of | #10796554, #10796560, #10796590, … |
| maximal quotient of | C22×#4802, C22×#4771, C22×#4861, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19752);