Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#5063 |
| 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)(6,9,10,7)(8,11,12,13)(14,16,18,23)(15,19,21,28)(17,26,27,24)(20,29,25,22);(1,2)(6,8,10,12)(7,11,9,13)(16,23)(19,28)(22,29)(24,26);(4,5)(6,7,10,9)(8,11,12,13)(14,15,18,21)(16,22,23,29)(17,25,27,20)(19,26,28,24);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10691540, #10691546, C4×#5063, … |
| maximal normal subgroup of | #10691540, #10691546, C4×#5063, … |
| maximal quotient of | C2×#69559, C2×#69631, C2×#69632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15596);