Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#4829 |
| Sylow | C3 ⋊ C2×#479 |
384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 4 generators on 29 points:
(3,4,5)(8,12)(10,13)(14,16,17,24,18,23,26,27)(15,19,20,22,21,28,25,29);(1,2)(6,8,9,12)(7,10,11,13)(16,23)(19,28)(22,29)(24,27);(4,5)(6,7,9,11)(8,10,12,13)(14,15,18,21)(16,22,23,29)(17,25,26,20)(19,27,28,24);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10691542, #10691544, #10802803, … |
| maximal normal subgroup of | #10691542, #10691544, #10802803, … |
| maximal quotient of | C2×#70486, C2×#68683, C2×#68684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11612);