Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#4772 |
| Fitting | C2×C3×#102 ⋊ C2 |
| Sylow | C3 ⋊ C2×#416 |
792 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 229 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)(7,9)(10,13,14,24,16,23,15,12)(11,18,19,17,21,25,20,22);(6,7)(8,9)(10,12)(11,17)(13,15)(14,23)(16,24)(18,19)(20,25)(21,22);(1,2)(4,5)(10,11)(12,22)(13,18)(14,19)(15,20)(16,21)(17,24)(23,25);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4772, #10792954, #10792984, … |
| maximal normal subgroup of | C4×#4772, #10792954, #10792984, … |
| maximal quotient of | C2×#68165, C2×#68173, #10761594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11315);