Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×C4×D4 ⋊ C2 |
| Sylow | C3 ⋊ #3109 |
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(4,6,7,10)(5,9,8,11)(12,14,15,16)(13,19,17,18);(13,18)(14,16)(17,19);(5,8)(9,11)(13,17)(18,19);(2,3)(4,5)(6,9)(7,8)(10,11)(12,13)(14,19)(15,17)(16,18)Polycyclic presentation:
2^7,3|d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,d^c=dg,f^c=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10691008, #10691010, #10692094, … |
| maximal normal subgroup of | #10691008, #10691010, #10692094, … |
| maximal quotient of | #10795231, #10798218, #10800078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14886);