Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4985 |
| Sylow | C3 ⋊ C2×#400 |
604 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 237 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:
(3,4,5)(6,7)(8,9)(10,12,13,16)(11,15,14,17)(20,25)(22,24);(1,2)(10,11)(12,15)(13,14)(16,17)(18,20,21,25)(19,22,23,24);(4,5)(7,9)(11,14)(15,17)(18,19,21,23)(20,24,25,22);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10690218, #10690223, #10695429, … |
| maximal normal subgroup of | #10690218, #10690223, #10695429, … |
| maximal quotient of | C2×#71566, C2×#69414, C2×#71567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14745);