Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#5009 |
| Sylow | C3 ⋊ C2×#478 |
448 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(7,11)(8,13)(10,12);(1,2)(7,10)(11,12)(14,16,17,21)(15,18,19,20);(4,5)(6,7,9,10)(8,11,13,12)(14,15,17,19)(16,20,21,18);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10691534, #10691536, #10802786, … |
| maximal normal subgroup of | #10691534, #10691536, #10802786, … |
| maximal quotient of | C2×#71605, C2×#71606, C2×#71607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14871);