Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4757 |
| Sylow | C3 ⋊ C2×#440 |
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(3,4,5)(6,8,9,7)(10,11)(12,17)(13,14)(15,16);(1,2)(11,15)(12,16)(14,17);(4,5)(6,7,9,8)(11,14)(15,17);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4757, #10793682, #10793702, … |
| maximal normal subgroup of | C4×#4757, #10793682, #10793702, … |
| maximal quotient of | C2×#68150, C2×#68156, C2×#68159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11300);