Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#5173 |
| Fitting | C22×C3×SD16 ⋊ 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)(7,9)(10,12,14,20)(11,16,15,24)(13,22,23,19)(17,25,21,18);(1,2)(10,11)(12,18)(13,21)(14,15)(16,19)(17,23)(20,25)(22,24);(4,5)(6,7)(8,9)(11,15)(16,24)(17,21)(18,25);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#5173, #10800820, #10800885, … |
| maximal normal subgroup of | C4×#5173, #10800820, #10800885, … |
| maximal quotient of | C2×#70974, C2×#71170, C2×#70973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16434);