Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#824 |
| Sylow | C3 ⋊ C4×#101 |
296 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(8,10,11,17,12,18,20,23)(9,13,14,21,15,16,19,22);(2,3)(8,9,12,15)(10,16,18,13)(11,19,20,14)(17,21,23,22);(4,5,6,7)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10685749, C8×#824, #10685759, … |
| maximal normal subgroup of | #10685749, C8×#824, #10685759, … |
| maximal quotient of | C4×#4469, #10685702, #10685706, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2446);