Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D4×D24 |
| Fitting | C3×C8×D4 ⋊ C2 |
| Sylow | C3 ⋊ D4×D8 |
620 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 620 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) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(8,9,13,15,11,14,10,12);(2,3)(9,12)(10,13)(14,15);(5,7);(4,5)(6,7)75 conjugacy classes — view the full character table.
| maximal subgroup of | #10708609, #10708613, #10708637, … |
| maximal normal subgroup of | #10708609, #10708613, #10708637, … |
| maximal quotient of | #10784536, #10784551, #10784566, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12008);