Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | #41×C3⋊C8 |
| Sylow | C3 ⋊ C8×#41 |
456 conjugacy classes of subgroups; only the 305 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 305 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(2,3)(4,5,6,8,7,9,10,11);(1,2,3)(12,14,15,18)(13,17,16,19);(13,16)(17,19);(12,13)(14,17)(15,16)(18,19)120 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×#104, #10685898, #10685903, … |
| maximal normal subgroup of | C3⋊C8×#104, #10685898, #10685903, … |
| maximal quotient of | C3⋊C8×#117, C4×D4×C3⋊C8, C4×Q8×C3⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15092);