Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#4888 |
| Fitting | C2×C3×#107 ⋊ C2 |
| Sylow | C3 ⋊ C2×#485 |
416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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)(7,11)(10,13)(14,16,23,29,18,24,17,22)(15,20,26,27,19,25,21,28);(1,2)(6,8,9,12)(7,10,11,13)(15,19)(16,22)(17,23)(20,27)(24,29)(25,28);(4,5)(6,7)(8,10)(9,11)(12,13)(14,15)(16,20)(17,21)(18,19)(22,28)(23,26)(24,25)(27,29);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10802352, C4×#4888, #10802426, … |
| maximal normal subgroup of | #10802352, C4×#4888, #10802426, … |
| maximal quotient of | C2×#68873, C2×#70633, C2×#68879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11728);