Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#5120 |
| Sylow | C3 ⋊ C2×#419 |
752 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 25 points:
(3,4,5)(7,9)(10,12,13,18,14,20,21,25)(11,15,16,22,17,19,23,24);(1,2)(10,11,14,17)(12,19,20,15)(13,16,21,23)(18,24,25,22);(4,5)(6,7,8,9)(12,18)(13,21)(15,22)(16,23)(19,24)(20,25);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10700675, #10700677, #10700736, … |
| maximal normal subgroup of | #10700675, #10700677, #10700736, … |
| maximal quotient of | C2×#70767, C2×#69857, #10761635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16350);