Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#5225 |
| Sylow | C3 ⋊ C2×#419 |
752 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 309 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)(11,15,17,19)(13,22,21,18)(16,25,24,23);(1,2)(10,11,14,17)(12,19,20,15)(13,16,21,24)(18,25,22,23);(4,5)(6,7,8,9)(12,18)(13,21)(15,23)(16,24)(19,25)(20,22);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10700676, #10700678, #10700737, … |
| maximal normal subgroup of | #10700676, #10700678, #10700737, … |
| maximal quotient of | C2×#71621, C2×#71623, #10761634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16632);