Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#5045 |
| Sylow | C3 ⋊ C2×#485 |
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 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) = 192 |
A minimal faithful permutation representation — 4 generators on 29 points:
(3,4,5)(6,8)(7,10)(9,12)(11,13)(14,17,19,16)(15,21,23,29)(18,24,28,26)(20,27,25,22);(1,2)(8,12)(10,13)(14,16,19,17)(15,20,23,25)(18,24,28,26)(21,27,29,22);(4,5)(6,7,9,11)(8,10,12,13)(14,15)(16,20)(17,25)(18,27)(19,23)(21,26)(22,28)(24,29);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10691498, #10691504, C4×#5045, … |
| maximal normal subgroup of | #10691498, #10691504, C4×#5045, … |
| maximal quotient of | C2×#69503, C2×#69506, C2×#71693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15301);