Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C22×D3×C22⋊C4 |
| Fitting | C22×C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C23×C22⋊C4 |
4632 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1157 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 — 5 generators on 15 points:
(5,6,7)(8,9)(10,11)(12,13)(14,15);(9,11)(12,13,14,15);(1,2)(3,4)(6,7);(3,4);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10686512, #10700447, #10700483, … |
| maximal normal subgroup of | #10686512, #10700447, #10700483, … |
| maximal quotient of | C22×D3×#95, C2×C4×D3×C22⋊C4, C22×#4666, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18265);