Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#5187 |
| Fitting | C22×C3×Q16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#452 |
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 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) = 25 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(3,4,5)(10,12,14,18)(11,15,17,24)(13,22,23,20)(16,25,21,19);(1,2)(7,9)(10,11,14,17)(12,19,18,25)(13,21,23,16)(15,22,24,20);(4,5)(6,7)(8,9)(12,18)(15,24)(19,25)(20,22);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#5187, #10800824, #10800889, … |
| maximal normal subgroup of | C4×#5187, #10800824, #10800889, … |
| maximal quotient of | C2×#70982, C2×#71178, C2×#70981, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16459);