Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4810 |
| Fitting | C2×C3×#103 ⋊ C2 |
| Sylow | C3 ⋊ C2×#449 |
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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)(10,11,13,14)(12,17,16,15);(1,2)(6,8,9,7)(11,15)(12,16)(14,17);(4,5)(6,7)(8,9)(11,14)(15,17);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10800801, C4×#4810, #10800875, … |
| maximal normal subgroup of | #10800801, C4×#4810, #10800875, … |
| maximal quotient of | C2×#68324, C2×#68328, C2×#68317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11369);