Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5189 |
| Fitting | C22×C3×Q16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#470 |
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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:
(3,4,5)(6,7)(8,9)(10,12,14,20)(11,16,15,23)(13,21,22,19)(17,25,24,18);(1,2)(10,11,13,17,14,15,22,24)(12,18,19,23,20,25,21,16);(1,2)(4,5)(7,9)(11,15)(16,23)(17,24)(18,25);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10712173, #10712224, #10713960, … |
| maximal normal subgroup of | #10712173, #10712224, #10713960, … |
| maximal quotient of | C2×#71306, C2×#71374, C2×#71235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16462);