Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#5000 |
| Sylow | C3 ⋊ C2×#433 |
412 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 229 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) = 192 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2)(3,4,5)(6,8)(7,10)(9,12)(11,13)(14,16)(15,19)(17,23)(18,22)(20,26)(21,25)(24,28)(27,29);(6,7,9,11)(8,10,12,13)(16,22)(19,25)(23,28)(26,29);(4,5)(8,12)(10,13)(14,15,17,20,18,21,24,27)(16,19,23,26,22,25,28,29);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10685725, #10688054, C4×#5000, … |
| maximal normal subgroup of | #10685725, #10688054, C4×#5000, … |
| maximal quotient of | C2×#69435, C2×#71582, C2×#69436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14784);