Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#127 ⋊ C2 |
| Sylow | C3 ⋊ #3038 |
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(8,10,12,11)(9,13,14,15);(2,3)(8,9)(10,13)(11,15)(12,14);(4,5,6,7);(5,7)(9,13)(10,11)(14,15)Polycyclic presentation:
2^7,3|b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,f^c=fg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10691077, #10691083, #10691084, … |
| maximal normal subgroup of | #10691077, #10691083, #10691084, … |
| maximal quotient of | #10779069, #10779078, #10779085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15741);