Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#833 |
| Sylow | C3 ⋊ C22×#100 |
992 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 309 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:
(5,6,7)(9,12)(10,14);(6,7)(8,9,10,13,11,12,14,15);(3,4);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10700504, #10700505, #10700549, … |
| maximal normal subgroup of | #10700504, #10700505, #10700549, … |
| maximal quotient of | C22×#4525, C2×#71601, C2×#71539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16612);