Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D4×Dic12 |
| Sylow | C3 ⋊ D4×Q16 |
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 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) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(8,10,17,21,12,19,11,18)(9,13,20,23,15,22,14,16);(2,3)(8,9,12,15)(10,16,19,23)(11,20,17,14)(13,21,22,18);(5,7);(4,5)(6,7)75 conjugacy classes — view the full character table.
| maximal subgroup of | #10708623, #10708627, #10708651, … |
| maximal normal subgroup of | #10708623, #10708627, #10708651, … |
| maximal quotient of | #10785376, #10785391, #10785406, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12021);