Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4853 |
| Sylow | C3 ⋊ C2×#441 |
480 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 197 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) = 384 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(3,4,5)(6,8,9,7)(10,12,14,20)(11,15,17,18)(13,22,21,19)(16,25,24,23);(1,2)(6,8,9,7)(12,19)(13,21)(15,23)(16,24)(18,25)(20,22);(4,5)(6,7,9,8)(10,11,14,17)(12,18,20,15)(13,16,21,24)(19,25,22,23);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10710463, #10710465, #10711930, … |
| maximal normal subgroup of | #10710463, #10710465, #10711930, … |
| maximal quotient of | C2×#68517, C2×#68522, C2×#68524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11680);