Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#4996 |
| 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)(6,8,9,12)(7,11,10,13)(15,20)(17,25)(19,26)(21,22)(23,29)(27,28);(1,2)(7,10)(11,13)(14,16,18,24)(15,19,22,28)(17,23,25,29)(20,26,21,27);(4,5)(6,7,9,10)(8,11,12,13)(14,15)(16,19)(17,20)(18,22)(21,25)(23,26)(24,28)(27,29);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10691499, #10691501, #10802348, … |
| maximal normal subgroup of | #10691499, #10691501, #10802348, … |
| maximal quotient of | C2×#71575, C2×#71576, C2×#71585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14795);