Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#833 |
| Sylow | C3 ⋊ C4×#100 |
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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 — 3 generators on 15 points:
(1,2,3)(9,12)(10,14);(2,3)(8,9,10,13,11,12,14,15);(4,5,6,7)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10682181, #10682182, #10682396, … |
| maximal normal subgroup of | #10682181, #10682182, #10682396, … |
| maximal quotient of | C4×#4525, #10685697, #10685710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4192);