Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#4703 |
| Sylow | C3 ⋊ C2×#491 |
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 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) = 29 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 4 generators on 29 points:
(3,4,5)(7,11)(10,12)(14,16,24,28,18,23,17,25)(15,20,26,29,19,27,21,22);(1,2)(6,8,9,13)(7,10,11,12)(15,19)(16,23)(21,26)(25,28);(4,5)(6,7,9,11)(8,12,13,10)(14,15,18,19)(16,22,23,29)(17,26,24,21)(20,28,27,25);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10690130, #10696500, #10696501, … |
| maximal normal subgroup of | #10690130, #10696500, #10696501, … |
| maximal quotient of | C2×#69815, C2×#69817, C2×#69822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11078);